Gravity Books

Book SynopsisBased on a course taught for years at Oxford, this book offers a concise exposition of the central ideas of general relativity. The focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. Includes links to recent developments, including theoretical work and observational evidence, to encourage further study.Trade ReviewFrom the reviews:“This book introduces General Relativity at students level, especially intended for final year mathematics students. Different from other books with the same title, it really goes into the geometric details and tries to explain the given formulae … . The appendices present exercises and hints to their solutions.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, May, 2014)"I have the opportunity to comment on General Relativity … . I am happy to recommend … for an advanced undergraduate course on relativity or for self-study. … marvelous faithfulness to historical developments … characterizes the entire treatment. … In fact, the whole book is distinguished by this high quality of exposition. … It’s a fine book, beautifully written and clear, and I highly recommend it." (Michael Berg, MathDL, January, 2007)MAA Reviews:In December, 2003 I had the pleasure of reviewing the admirable book Special Relativity, by N.M.J. Woodhouse, and now I have the opportunity to comment on General Relativity by the same author. I am happy to recommend not just this sequel, but the indicated pair, for an advanced undergraduate course on relativity or for self-study.One particularly noteworthy feature of General Relativity is that woodhouse seeks to present the subject neither as a branch of differential geometry nor as the kind of physics mathematicians like me find unapproachable (and I'm afraid this doesn't particularly narrow the field). When just a rookie I dabbled in relativity largely from popularizations and biographical writings, and when I tried to learn some real general relativity in graduate school - for cultural reasons, I guess - it simply didn't take. But my interest in the subject, both specially and generally, has never flagged and Woodhouse’s books are tailor-made for even my lingering ambitions. In other words, for any slacker who feels he should have learned this beautiful material in his mathematical youth, but didn’t, and is now secretly (or not so secretly) desirous of doing it right, this is the book, or, more correctly, these are the books to read. Furthermore, as I already hinted, as far as teaching courses on these important subjects is concerned, obviously these books fit that bill very well too, given Woodhouse’s specific pedagogical intent.When it comes to the specific style and presentation of general relativity chosen by Woodhouse, marvellous faithfulness to historical developments, in particular Einstein’s own writings, characterizes the entire treatment. On p.7, already, the weak and strong equivalence principles are presented and analysed in a succinct and historically rooted fashion. The former, going back to Galileo’s pendulums (Woodhouse correctly says "pendula," of course) and famously connected with Eötvös’ experiment, entails that inertial mass and gravitational mass are the same; and the latter says that there are no obvservable differences between the local effects of gravity and acceleration. Woodhouse’s brief discussion of these observable differences between the local effects of gravity and acceleration. Woodhouse’s brief discussion of these incomparable axioms underlying Einstein’s revolution is a gem of exposition, covering the historical sweep of the attendant experiments (he even mentions a planned space experiment, "STEP," which will test the latter principle to within one part in 1018) and conveying what is to come as a result of these stipulations. Finally, I want to draw special attention to pp.23-27, where Woodhouse does a phenomenally good job of explicating the subject of tensors in Minkowski space, a subject which has always been a bit unsettling to me who was raised to visit tensor products in their homological algebraic home and I cannot resist mentioning Problem 1.5 on p.13, dealing with "Einstein’s birthday present."It’s a fine book, beautifully written and clear, and I highly recommend it. [Reviewed by Michael Berg, 20.1.2007]"Woodhouse … lets the physical intuition behind relativity inform every step of its logical development, making his treatment as digestible as any in print. He does introduce ab ovo what differential geometry he needs, and he takes the whole theory far enough to develop general relativity’s most exciting predictions, black holes and gravity waves, all in less than half the number of pages one might expect. Summing Up: Highly recommended. Upper-division undergraduates through professionals." (D. V. Feldman, CHOICE, Vol. 44 (11), July, 2007)"The book is an outgrowth of a lecture course given over many years by the author and his colleagues to final-year applied mathematicians at the Mathematical Institute in Oxford, UK. The book is well-written and easy to follow because the author constructs the necessary apparatus layer-by-layer, from the bottom up, carefully motivating and justifying every new concept. Exercises are given at the end of every chapter … and numerous examples appear throughout the text. … its expository style is very appealing." (David A. Burton, General Relativity and Gravitation, Vol. 39, 2007)Table of ContentsNewtonian Gravity.- Inertial Coordinates and Tensors.- Energy-Momentum Tensors.- Curved Space—Time.- Tensor Calculus.- Einstein’s Equation.- Spherical Symmetry.- Orbits in the Schwarzschild Space—Time.- Black Holes.- Rotating Bodies.- Gravitational Waves.- Redshift and Horizons.

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Book SynopsisThis book provides readers with the tools needed to understand the physical basis of special relativity and will enable a confident mathematical understanding of Minkowski's picture of space-time. It features a large number of examples and exercises, ranging from the rather simple through to the more involved and challenging. Coverage includes acceleration and tensors and has an emphasis on space-time diagrams.Trade ReviewFrom the reviews: N.M.J. Woodhouse's comparatively short Special Relativity is a pleasure to read and therefore qualifies right off as a good source to use for learning about special relativity on your own. A lot of very nice material is touched on in its pages, presented in natural sequence consonant with history, and is not improperly belabored. It's also rather informal in style. One gets the sense of breezing along pretty fast while, in actuality, a lot of material is being dealt with... the selection of topics in the book is very nice indeed , and is historically sound and will therefore reward the reader with an element of culture to boot: he'll learn some history of modern physics... I wish this book had been around when I was a student. MAA Online ...an exciting and challenging book with which to introduce a modern mathematics student in a single course to the great ideas of Maxwell's theory and special relativity. The Australian Mathematical Society Gazette "There are many books on special relativity for undergraduates, and this one is notable in that it is specifically addressed to mathematicians. … this book will be found illuminating by students of mathematics … ." (Dr. P. E. Hodgson, Contemporary Physics, Vol. 45 (5), 2004) "This book is … aimed squarely at the undergraduate mathematician ... . The tone, pace and level of the book are nicely judged for middle level undergraduates studying mathematics. … There are lots of examples and nicely graded exercises throughout the text, and each chapter ends with a usefully annotated bibliography. The author’s friendly style, and the fact the material has been developed from taught courses make the book ideal for self-study … ." (Peter Macgregor, The Mathematical Gazette, Vol. 88 (512), 2004) "Meant as a resource for advanced undergraduate students, this book approaches special relativity theory from a mathematical perspective … . It is best used for mathematics majors … . the text is clear, well written, and has an adequate bibliography. Summing Up: Recommended. Upper-division undergraduates." (A. Spero, CHOICE, December, 2003) "This presentation is very elegant … . The book contains a large number of examples. Each chapter is followed by exercises, ranging from the rather simple to the more involved. This book is certainly a good introduction to special relativity, understandable for second-year students. But it is also interesting for readers searching for a concise and precise presentation of special relativity within the tensor formalism." (Claude Semay, Physcalia, Vol. 25 (4), 2003)Table of Contents1. Relativity in Classical Mechanics.- 1.1 Frames of Reference.- 1.2 Relativity.- 1.3 Frames of Reference.- 1.4 Newton’s Laws.- 1.5 Galilean Transformations.- 1.6 Mass, Energy, and Momentum.- 1.7 Space-time.- 1.8 *Galilean Symmetries.- 1.9 Historical Note.- 2. Maxwell’s Theory.- 2.1 Introduction.- 2.2 The Unification of Electricity and Magnetism.- 2.3 Charges, Fields, and the Lorentz Force Law.- 2.4 Stationary Distributions of Charge.- 2.5 The Divergence of the Magnetic Field.- 2.6 Inconsistency with Galilean Relativity.- 2.7 The Limits of Galilean Invariance.- 2.8 Faraday’s Law of Induction.- 2.9 The Field of Charges in Uniform Motion.- 2.10 Maxwell’s Equations.- 2.11 The Continuity Equation.- 2.12 Conservation of Charge.- 2.13 Historical Note.- 3. The Propagation of Light.- 3.1 The Displacement Current.- 3.2 The Source-free Equations.- 3.3 The Wave Equation.- 3.4 Monochromatic Plane Waves.- 3.5 Polarization.- 3.6 Potentials.- 3.7 Gauge Transformations.- 3.8 Photons.- 3.9 Relativity and the Propagation of Light.- 3.10 The Michelson-Morley Experiment.- 4. Einstein’s Special Theory of Relativity.- 4.1 Lorentz’s Contraction.- 4.2 Operational Definitions of Distance and Time.- 4.3 The Relativity of Simultaneity.- 4.4 Bondi’s fc-Factor.- 4.5 Time Dilation.- 4.6 The Two-dimensional Lorentz Transformation.- 4.7 Transformation of Velocity.- 4.8 The Lorentz Contraction.- 4.9 Composition of Lorentz Transformations.- 4.10 Rapidity.- 4.11 *The Lorentz and Poincaré Groups.- 5. Lorentz Transformations in Four Dimensions.- 5.1 Coordinates in Four Dimensions.- 5.2 Four-dimensional Coordinate Transformations.- 5.3 The Lorentz Transformation in Four Dimensions.- 5.4 The Standard Lorentz Transformation.- 5.5 The General Lorentz Transformation.- 5.6 Euclidean Space and Minkowski Space.- 5.7 Four-vectors.- 5.8 Temporal and Spatial Parts.- 5.9 The Inner Product.- 5.10 Classification of Four-vectors.- 5.11 Causal Structure of Minkowski Space.- 5.12 Invariant Operators.- 5.13 The Frequency Four-vector.- 5.14 * Affine Spaces and Covectors.- 6. Relative Motion.- 6.1 Transformations Between Frames.- 6.2 Proper Time.- 6.3 Four-velocity.- 6.4 Four-acceleration.- 6.5 Constant Acceleration.- 6.6 Continuous Distributions.- 6.7 *Rigid Body Motion.- 6.8 Visual Observation.- 7. Relativistic Collisions.- 7.1 The Operational Definition of Mass.- 7.2 Conservation of Four-momentum.- 7.3 Equivalence of Mass and Energy.- 8. Relativistic Electrodynamics.- 8.1 Lorentz Transformations of E and B.- 8.2 The Four-Current and the Four-potential.- 8.3 Transformations of E and B.- 8.4 Linearly Polarized Plane Waves.- 8.5 Electromagnetic Energy.- 8.6 The Four-momentum of a Photon.- 8.7 *Advanced and Retarded Solutions.- 9. *Tensors and Isomet ries.- 9.1 Affine Space.- 9.2 The Lorentz Group.- 9.3 Tensors.- 9.4 The Tensor Product.- 9.5 Tensors in Minkowski Space.- 9.6 Tensor Components.- 9.7 Examples of Tensors.- 9.8 One-parameter Subgroups.- 9.9 Isometries.- 9.10 The Riemann Sphere and Spinors.- Notes on Exercises.- Vector Calculus.

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Book Synopsis

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Book Synopsis

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Book SynopsisBased on Prof. Lüst's Masters course at the University of Munich, this book begins with a short introduction to general relativity. It then presents black hole solutions, and discusses Penrose diagrams, black hole thermodynamics and entropy, the Unruh effect, Hawking radiation, the black hole information problem, black holes in supergravity and string theory, the black hole microstate counting in string theory, asymptotic symmetries in general relativity, and a particular quantum model for black holes. The book offers an up-to-date summary of all the pertinent questions in this highly active field of physics, and is ideal reading for graduate students and young researchers.Table of ContentsSpecial relativity.- Riemannian geometry.- Introduction to general relativity.- General relativity.- Einstein's equations.- Black holes.- Kruskal-Szekeres coordinates and geodesics of the Schwarzschild black hole.- Conformal compactifications and Penrose diagrams.- Penrose diagrams of charged & rotating black holes.- Rotating black holes and black hole mechanics.- Black hole mechanics and thermodynamics.- Black hole thermodynamics .- Black holes and entropy.- Hawking and Unruh radiation.- Quantum field theory in curved space-time backgrounds.- Unruh und Hawking effect.- Information loss paradox.- Solitons in String Theory.- Brane solutions.- Dimensional reduction and black holes.- Black holes in string theory from p/D-branes.- Black hole microstate counting.- Asymptotic symmetries in general relativity and black hole hair.- Asymptotic symmetries of 4D space-time geometries.- BMS charges.- The gravitational memory effect.- Current research on BMS-like transformations and charges of black holes.- Quantum hair and quantum black hole vacua.

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Book SynopsisThis book explains and develops the Dirac equation in the context of general relativistic quantum mechanics in a range of spacetime dimensions. It clarifies the subject by carefully pointing out the various conventions used and explaining how they are related to each other. The prerequisites are familiarity with general relativity and an exposure to the Dirac equation at the level of special relativistic quantum mechanics, but a review of this latter topic is given in the first chapter as a reference and framework for the physical interpretations that follow. Worked examples and exercises with solutions are provided. Appendices include reviews of topics used in the body of the text. This book should benefit researchers and graduate students in general relativity and in condensed matter.Trade Review“Ultimately, this short monograph will be of interest as a quick guide to researchers who need a notation reference, well organized overview of the literature, or an introduction to the subject, looking for connection with their own field; also for graduate students who are looking for a bird's eye view or need help with determining the learning path. It must be added that students especially will appreciate that the authors provide solutions to the exercises.” (Tomasz Artur Stachowiak, Mathematical Reviews, December, 2019)“The book represents a very useful tool for graduate students and beginning researchers in a large area of the theory and applications of the Dirac equation. It can be useful for all the stages of learning: from the initial acknowledgement to deep investigations. … The book will be very useful to everybody desiring to make an economy with special articles from various journals.” (Alex B. Gaina, zbMath 1416.81003, 2019)Table of ContentsIntroduction.- The Dirac equation in special relativity.- The spinorial covariant derivative.- Examples in (3+1) GR.- The Dirac equation in (1+1) GR.- The Dirac equation in (2+1) GR.- Scalar product.- Appendices.

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Book SynopsisCosmology describes the evolution of the Universe and is based on a description of its beginning from quantum fluctuations. String theory is the only known consistent theory of quantum gravity that can deal with the highest energy scales near the Planck energy, relevant for cosmology's beginning. As a result, only string theory can give a fully consistent picture of cosmological origins. This book describes the best current avenues for obtaining cosmology from string theory. It is aimed at graduate students, and also researchers, with some familiarity with cosmology and string theory, however no detailed knowledge is required. Table of Contents

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Book SynopsisThis primer brilliantly exposes concepts related to special and general relativity for the absolute beginner. It can be used either as an introduction to the subject at a high school level or as a useful compass for undergraduates who want to move the first steps towards Einstein's theories.The book is enhanced throughout with many useful exercises and beautiful illustrations to aid understanding.The topics covered include: Lorentz transformations, length contraction and time dilation, the twin paradox (and other paradoxes), Minkowski spacetime, the Einstein equivalence principle, curvature of space and spacetime, geodesics, parallel transport, Einstein’s equations of general relativity, black holes, wormholes, cosmology, gravitational waves, time machines, and much more.Table of Contents1 Introduction.- 2 Fundamentals of Math & Classical Mechanics.- 3 Special Relativity.- 4 General Relativity.- A Quick Reference.- B Answer to Select Problems.

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Book SynopsisIn the late 20th and beginning 21st century high-precision astronomy, positioning and metrology strongly rely on general relativity. Supported by exercises and solutions this book offers graduate students and researchers entering those fields a self-contained and exhaustive but accessible treatment of applied general relativity. The book is written in a homogenous (graduate level textbook) style allowing the reader to understand the arguments step by step. It first introduces the mathematical and theoretical foundations of gravity theory and then concentrates on its general relativistic applications: clock rates, clock sychronization, establishment of time scales, astronomical references frames, relativistic astrometry, celestial mechanics and metrology. The authors present up-to-date relativistic models for applied techniques such as Satellite LASER Ranging (SLR), Lunar LASER Ranging (LLR), Globale Navigation Satellite Systems (GNSS), Very Large Baseline Interferometry (VLBI), radar measurements, gyroscopes and pulsar timing. A list of acronyms helps the reader keep an overview and a mathematical appendix provides required functions and terms.Table of Contents

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Book SynopsisThis textbook develops Special Relativity in a systematic way and offers problems with detailed solutions to empower students to gain a real understanding of this core subject in physics. This new edition has been thoroughly updated and has new sections on relativistic fluids, relativistic kinematics and on four-acceleration. The problems and solution section has been significantly expanded and short history sections have been included throughout the book.The approach is structural in the sense that it develops Special Relativity in Minkowski space following the parallel steps as the development of Newtonian Physics in Euclidian space. A second characteristic of the book is that it discusses the mathematics of the theory independently of the physical principles, so that the reader will appreciate their role in the development of the physical theory.The book is intended to be used both as a textbook for an advanced undergraduate teaching course in Special Relativity but also as a reference book for the future. Table of ContentsMathematical Part.- The Structure of the Theories of Physics.- Newtonian Physics.- The Foundation of Special Relativity.- The Physics of the Position Four-Vector.- Relativistic Kinematics.- Four-Acceleration.- Paradoxes.- Mass – Four-Momentum.- Relativistic Reactions.- Four-Force.- Irreducible Decompositions.- The Electromagnetic Field.- Relativistic Angular Momentum.- The Covariant Lorentz Transformation.- Geometric Description of Relativistic Interactions.

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Book SynopsisThis primer is a collection of notes based on lectures that were originally given at IIT Madras (India) and at IFT Madrid (Spain). It is a concise and pragmatic course on applied holography focusing on the basic analytic and numerical techniques involved. The presented lectures are not intended to provide all the fundamental theoretical background, which can be found in the available literature, but they concentrate on concrete applications of AdS/CFT to hydrodynamics, quantum chromodynamics and condensed matter. The idea is to accompany the reader step by step through the various benchmark examples with a classmate attitude, providing details for the computations and open-source numerical codes in Mathematica, and sharing simple tricks and warnings collected during the author’s research experience. At the end of this path, the reader will be in possess of all the fundamental skills and tools to learn by him/herself more advanced techniques and to produce independent and novel research in the field.Table of ContentsA Strings-less introduction to AdS-CFT.- A Practical Understanding of the Dictionary.- The first big success: η/s and Hydrodynamics.- Holographic Transport via analytic and numerical techniques.

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Book SynopsisThe revised and updated 2nd edition of this established textbook provides a self-contained introduction to the general theory of relativity, describing not only the physical principles and applications of the theory, but also the mathematics needed, in particular the calculus of differential forms.Updated throughout, the book contains more detailed explanations and extended discussions of several conceptual points, and strengthened mathematical deductions where required. It includes examples of work conducted in the ten years since the first edition of the book was published, for example the pedagogically helpful concept of a "river of space" and a more detailed discussion of how far the principle of relativity is contained in the general theory of relativity. Also presented is a discussion of the concept of the 'gravitational field' in Einstein's theory, and some new material concerning the 'twin paradox' in the theory of relativity. Finally, the book contains a new section about gravitational waves, exploring the dramatic progress in this field following the LIGO observations. Based on a long-established masters course, the book serves advanced undergraduate and graduate level students, and also provides a useful reference for researchers.Table of ContentsNewton’s law of universal gravitation.- The force law of gravitation.- Newton’s law of gravitation in local form.- Tidal forces.- The principle of equivalence.- The general principle of relativity.- The covariance principle.- Mach’s principle.- The special theory of relativity.- Coordinate systems and Minkowski diagrams.- Synchronization of clocks.- The Doppler effect.- Relativistic time-dilation.- The relativity of simultaneity.- The Lorentz contraction.- The Lorentz transformation.- The Lorentz invariant interval.- The twin paradox.- Hyperbolic motion.- Energy and mass.- Relativistic increase of mass.- Tachyons.- Magnetism as a relativistic second order effect.- Vectors, tensors and forms.- Vectors.- Four-vectors.- Tangent vector fields and coordinate vectors.- Coordinate transformations.- Structure coefficients.- Tensors.- Transformation of tensor components.- Transformation of basis 1-forms.- The metric tensor.- Forms.- Rotating and accelerated reference frames.- Rotating reference frames.- The spatial metric tensor.- Angular acceleration of the rotating frame.- Gravitational time dilation.- Path of photons emitted from the axis in a rotating frame.- The Sagnac effect.- Uniformly accelerated reference frames.- Covariant differentiation.- Differentiation of forms.- Exterior differentiation.- Covariant derivative.- The Christoffel symbols.- Geodetic curves.- The covariant Euler-Lagrange equations.- Application of the Lagrange formalism to free particles.- Equation of motion from Lagrange’s equations.- Geodesic worldliness in spacetime.- Gravitational Doppler effect.- The Koszul connection.- Connection coefficients and structure coefficients in a Riemannian (torsion free) space.- Covariant differentiation of vectors, forms and tensors.- Covariant differentiation of a vector field in an arbitrary basis.- Covariant differentiation of forms.- Generalization for tensors of higher rank.- The Cartan connection.- Curvature.- The Riemann curvature tensor.- Differential geometry of surfaces.- Surface curvature using the Cartan formalism.- The Ricci identity.- Bianchi’s 1st identity.- Bianchi’s 2nd identity.- Einstein’s field equations.- Energy-momentum conservation.- Newtonian fluid.- Perfect fluids.- Einstein’s curvature tensor.- Einstein’s field equations.- The 'geodesic postulate' as a consequence of the field equations.- The Schwarschild spacetime.- Schwarzschild’s exterior solution.- Radial free fall in Schwarzschild spacetime.- Light cones in Schwarzschild spacetime.- Analytical extension of the Schwarzschild coordinates.- Embedding of the Schwarzschild metric.- Deceleration of light.- Particle trajectories in Schwarzschild 3-space.- Motion in the equatorial plane.- Classical tests of Einstein’s general theory of relativity.- The Hafele-Keating experiment.- Mercury’s perihelion precession.- Deflection of light.- Black holes.- 'Surface gravity': gravitational acceleration on the horizon of a black hole.- Hawking radiation: radiation from a black hole.- Rotating black holes: The Kerr metric.- Zero-angular-momentum-observers.- Does the Kerr space have a horizon?.- Schwarzschild’s interior solution.- Newtonian incompressible star.- The pressure contribution to the gravitational mass of a static, spherically symmetric system.- The Tolman-Oppenheimer-Volkov equation.- An exact solution for incompressible stars – Schwarzschild’s interior solution.- Cosmology.- Comoving coordinate system.- Curvature isotropy – the Robertson-Walker metric.- Cosmic dynamics.- Hubble’s law.- Cosmological redshift of light.- Cosmic fluids.- Isotropic and homogeneous universe models.- Some cosmological models.- Radiation dominated model.- Dust dominated model.- Transition from radiation to matter dominated universe.- Friegmann-Lemaître model.- Inflationary cosmology.- Problems with the Big Bang models.- Cosmic inflation.

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Book SynopsisThis book provides an in-depth and accessible description of special relativity and quantum mechanics which together form the foundation of 21st century physics. A novel aspect is that symmetry is given its rightful prominence as an integral part of this foundation. The book offers not only a conceptual understanding of symmetry, but also the mathematical tools necessary for quantitative analysis. As such, it provides a valuable precursor to more focused, advanced books on special relativity or quantum mechanics.Students are introduced to several topics not typically covered until much later in their education.These include space-time diagrams, the action principle, a proof of Noether's theorem, Lorentz vectors and tensors, symmetry breaking and general relativity. The book also provides extensive descriptions on topics of current general interest such as gravitational waves, cosmology, Bell's theorem, entanglement and quantum computing.Throughout the text, every opportunity is taken to emphasize the intimate connection between physics, symmetry and mathematics.The style remains light despite the rigorous and intensive content. The book is intended as a stand-alone or supplementary physics text for a one or two semester course for students who have completed an introductory calculus course and a first-year physics course that includes Newtonian mechanics and some electrostatics. Basic knowledge of linear algebra is useful but not essential, as all requisite mathematical background is provided either in the body of the text or in the Appendices. Interspersed through the text are well over a hundred worked examples and unsolved exercises for the student.Table of Contents1 Introduction 91.1 The goal of physics . . . . . . . . . . . . . . . . . . . . . . . . 91.2 The connection between physics and mathematics . . . . . . . 101.3 Paradigm shifts . . . . . . . . . . . . . . . . . . . . . . . . . . 131.4 The Correspondence Principle . . . . . . . . . . . . . . . . . . 162 Symmetry and Physics 172.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 172.2 What is Symmetry? . . . . . . . . . . . . . . . . . . . . . . . . 172.3 Role of Symmetry in Physics . . . . . . . . . . . . . . . . . . . 182.3.1 Symmetry as a guiding principle . . . . . . . . . . . . . 182.3.2 Symmetry and Conserved Quantities: Noether's Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.3 Symmetry as a tool for simplifying problems . . . . . . 192.4 Symmetries were made to be broken . . . . . . . . . . . . . . 202.4.1 Spacetime symmetries . . . . . . . . . . . . . . . . . . 202.4.2 Parity violation . . . . . . . . . . . . . . . . . . . . . . 212.4.3 Spontaneously broken symmetries . . . . . . . . . . . . 242.4.4 Variational calculations: Lifeguards and light rays . . . 273 Formal Aspects of Symmetry 303.1 Learning outcomes . . . . . . . . . . . . . . . . . . . . . . . . 303.2 Symmetries and Operations . . . . . . . . . . . . . . . . . . . 303.2.1 Denition of a symmetry operation . . . . . . . . . . . 303.2.2 Rules obeyed by symmetry operations . . . . . . . . . 323.2.3 Multiplication tables . . . . . . . . . . . . . . . . . . . 353.2.4 Symmetry and group theory . . . . . . . . . . . . . . . 363.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3.1 The identity operation . . . . . . . . . . . . . . . . . . 373.3.2 Permutations of two identical objects . . . . . . . . . . 373.3.3 Permutations of three identical objects . . . . . . . . . 383.3.4 Rotations of regular polygons . . . . . . . . . . . . . . 393.4 Continuous vs discrete symmetries . . . . . . . . . . . . . . . 403.5 Symmetries and Conserved Quantities:Noether's Theorem . . . . . . . . . . . . . . . . . . . . . . . . 413.6 Supplementary: Variational Mechanics and the Proof of Noether'sTheorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.6.1 Variational Mechanics: Principle of Least Action . . . . 423.6.2 Euler-Lagrange Equations . . . . . . . . . . . . . . . . 473.6.3 Proof of Noether's Theorem . . . . . . . . . . . . . . . 484 Symmetries and Linear Transformations 524.1 Learning outcomes . . . . . . . . . . . . . . . . . . . . . . . . 524.2 Review of Vectors . . . . . . . . . . . . . . . . . . . . . . . . . 534.2.1 Coordinate free denitions . . . . . . . . . . . . . . . . 534.2.2 Cartesian Coordinates . . . . . . . . . . . . . . . . . . 584.2.3 Vector operations in component form . . . . . . . . . . 594.2.4 Position vector . . . . . . . . . . . . . . . . . . . . . . 604.2.5 Dierentiation of vectors: velocity and acceleration . . 624.3 Linear Transformations . . . . . . . . . . . . . . . . . . . . . . 634.3.1 Denition . . . . . . . . . . . . . . . . . . . . . . . . . 634.3.2 Translations . . . . . . . . . . . . . . . . . . . . . . . . 644.3.3 Rotations . . . . . . . . . . . . . . . . . . . . . . . . . 664.3.4 Reections . . . . . . . . . . . . . . . . . . . . . . . . . 674.4 Linear Transformations and matrices . . . . . . . . . . . . . . 684.4.1 Linear transformations as matrices . . . . . . . . . . . 684.4.2 Identity Transformation and Inverses . . . . . . . . . . 704.4.3 Rotations . . . . . . . . . . . . . . . . . . . . . . . . . 704.4.4 Reections . . . . . . . . . . . . . . . . . . . . . . . . . 724.4.5 Matrix Representation of Permutations of Three Objects 734.5 Pythagoras and Geometry . . . . . . . . . . . . . . . . . . . . 745 Special Relativity I: The Basics 775.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 775.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 775.2.1 Frames5.2.2 Spacetime Diagrams . . . . . . . . . . . . . . . . . . . 785.2.3 Newtonian Relativity and Galilean Transformations . . 835.3 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.3.1 The Fundamental Postulate . . . . . . . . . . . . . . . 855.3.2 The problem with Galilean Relativity . . . . . . . . . . 855.3.3 Michelson-Morley Experiment . . . . . . . . . . . . . . 875.3.4 Maxwell's Equations . . . . . . . . . . . . . . . . . . . 905.4 Summary of Consequences . . . . . . . . . . . . . . . . . . . . 915.5 Relativity of Simultaneity . . . . . . . . . . . . . . . . . . . . 925.6 Time Dilation . . . . . . . . . . . . . . . . . . . . . . . . . . . 975.6.1 Derivation: . . . . . . . . . . . . . . . . . . . . . . . . 975.6.2 Proper Time . . . . . . . . . . . . . . . . . . . . . . . . 995.6.3 Experimental Conrmation . . . . . . . . . . . . . . . 1015.6.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . 1025.7 Lorentz Contraction . . . . . . . . . . . . . . . . . . . . . . . 1045.7.1 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . 1045.7.2 Properties: . . . . . . . . . . . . . . . . . . . . . . . . . 1045.7.3 Proper Length and Proper Distance. . . . . . . . . . . 1045.7.4 Examples: . . . . . . . . . . . . . . . . . . . . . . . . . 1056 Special Relativity II: In Depth 1106.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 1106.2 Lorentz Transformations . . . . . . . . . . . . . . . . . . . . . 1106.2.1 Derivation of general form . . . . . . . . . . . . . . . . 1106.2.2 Properties of Lorentz Transformations . . . . . . . . . 1136.2.3 Lorentzian Geometry . . . . . . . . . . . . . . . . . . . 1166.3 The Light Cone . . . . . . . . . . . . . . . . . . . . . . . . . . 1196.4 Proper time revisited . . . . . . . . . . . . . . . . . . . . . . . 1206.5 Relativistic Addition of Velocities . . . . . . . . . . . . . . . . 1226.6 Relativistic Doppler Shift . . . . . . . . . . . . . . . . . . . . . 1246.6.1 Non-relativistic Doppler Shift Review . . . . . . . . . . 1246.6.2 Relativistic Doppler Shift . . . . . . . . . . . . . . . . 1246.7 Relativistic Energy and Momentum . . . . . . . . . . . . . . . 1276.7.1 Relativistic Energy Momentum Conservation . . . . . . 1276.7.2 Relativistic Inertia . . . . . . . . . . . . . . . . . . . . 1286.7.3 Relativistic Energy . . . . . . . . . . . . . . . . . . . . 1296.7.4 Relativistic Three-Momentum . . . . . . . . . . . . . . 1296.7.5 Relationship Between Relativistic Energy and Momentum. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1306.7.6 Kinetic energy: . . . . . . . . . . . . . . . . . . . . . . 1306.7.7 Massless particles . . . . . . . . . . . . . . . . . . . . 1316.8 Space-time Vectors . . . . . . . . . . . . . . . . . . . . . . . . 1336.8.1 Position Four-Vector: . . . . . . . . . . . . . . . . . . . 1346.8.2 Four-momentum: . . . . . . . . . . . . . . . . . . . . . 1356.8.3 Null four-vectors . . . . . . . . . . . . . . . . . . . . . 1376.8.4 Relativistic Scattering . . . . . . . . . . . . . . . . . . 1376.8.5 More Examples . . . . . . . . . . . . . . . . . . . . . . 1386.9 Relativistic Units . . . . . . . . . . . . . . . . . . . . . . . . . 1396.10 Symmetry Redux . . . . . . . . . . . . . . . . . . . . . . . . . 1406.10.1 Matrix form of Lorentz Transformations . . . . . . . . 1406.10.2 Lorentz Transformations as a Symmetry Group . . . . 1426.11 Supplementary: Four vectors and tensors in covariant form . . 1437 General Relativity 1497.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 1497.2 Problems with Newtonian Gravity . . . . . . . . . . . . . . . . 1497.2.1 Review of Newtonian Gravity . . . . . . . . . . . . . . 1497.2.2 Perihelion Shift of Mercury . . . . . . . . . . . . . . . 1517.2.3 Action at a Distance . . . . . . . . . . . . . . . . . . . 1527.2.4 The Puzzle of Inertial vs Gravitational Mass . . . . . . 1537.3 Einstein's Thinking: the Strong Principle of Equivalence . . . 1537.4 Geometry of Spacetime . . . . . . . . . . . . . . . . . . . . . . 1557.5 Some Consequences of General Relativity: . . . . . . . . . . . 1587.6 Gravitational Waves . . . . . . . . . . . . . . . . . . . . . . . 1597.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 1597.6.2 Detection . . . . . . . . . . . . . . . . . . . . . . . . . 1607.6.3 Recent Observations . . . . . . . . . . . . . . . . . . . 1617.7 Black Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1637.7.1 Denition . . . . . . . . . . . . . . . . . . . . . . . . . 1637.7.2 Properties: . . . . . . . . . . . . . . . . . . . . . . . . . 1637.7.3 Observational Evidence . . . . . . . . . . . . . . . . . . 1647.7.4 Further Information . . . . . . . . . . . . . . . . . . . 1667.8 Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1668 Introduction to the Quantum 1708.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 1708.2 Light as particles . . . . . . . . . . . . . . . . . . . . . . . . . 1718.2.1 Review: Light as Waves . . . . . . . . . . . . . . . . . 1718.2.2 Photoelectric Eect . . . . . . . . . . . . . . . . . . . . 1718.2.3 Compton Scattering . . . . . . . . . . . . . . . . . . . 1758.3 Blackbody Radiation and the Ultraviolet Catastrophe . . . . . 1798.3.1 Blackbody Radiation . . . . . . . . . . . . . . . . . . . 1798.3.2 Derivation of Rayleigh-Jeans Law . . . . . . . . . . . . 1818.3.3 The ultraviolet catastrophe . . . . . . . . . . . . . . . 1888.3.4 Quantum resolution: . . . . . . . . . . . . . . . . . . . 1898.3.5 The Early Universe: the ultimate blackbody . . . . . . 1918.4 Particles as waves . . . . . . . . . . . . . . . . . . . . . . . . . 1968.4.1 Electron waves . . . . . . . . . . . . . . . . . . . . . . 1968.4.2 de Broglie Wavelength . . . . . . . . . . . . . . . . . . 1978.4.3 Observational Evidence . . . . . . . . . . . . . . . . . . 1998.5 The Heisenberg Uncertainty Principle . . . . . . . . . . . . . . 2029 The Wave Function 2049.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 2049.2 Quantum vs Newtonian description of physical states . . . . . 2049.2.1 Newtonian description of the state of a particle . . . . 2059.2.2 Quantum description of the state of a particle . . . . . 2059.3 Physical Consequences and Interpretation . . . . . . . . . . . 2079.4 Measurements of position . . . . . . . . . . . . . . . . . . . . 2089.5 Example: Gaussian wavefunction . . . . . . . . . . . . . . . . 2099.6 \Spooky" Action at a Distance: Non-Locality in QuantumMechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2119.6.1 The EPR \Paradox" . . . . . . . . . . . . . . . . . . . 2119.6.2 Bell's Theorem and the Experimental Repudiation ofEPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21410 The Schrodinger Equation 21710.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 21710.2 Momentum in Quantum Mechanics . . . . . . . . . . . . . . . 21810.2.1 Pure Waves . . . . . . . . . . . . . . . . . . . . . . . . 21810.2.2 The Momentum Operator . . . . . . . . . . . . . . . . 22010.3 Energy in Quantum Mechanics . . . . . . . . . . . . . . . . . 22310.4 The Time Independent Schrodinger Equation . . . . . . . . . 22410.4.1 Stationary States . . . . . . . . . . . . . . . . . . . . . 22410.4.2 The \Quantum" in Quantum Mechanics . . . . . . . . 22610.5 Examples of Stationary States . . . . . . . . . . . . . . . . . . 22610.5.1 Free particle in one dimension . . . . . . . . . . . . . . 22610.5.2 Example 2: Particle in a Box with Impenetrable Walls 22710.5.3 Example 3 : Simple Harmonic Oscillator . . . . . . . . 22910.6 Absorption and emission . . . . . . . . . . . . . . . . . . . . . 23110.7 Tunnelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23310.7.1 Tunnelling through a potential barrier of nite width . 23310.7.2 Particle in a Box with Penetrable Walls . . . . . . . . . 23510.7.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . 23710.7.4 Applications of tunnelling . . . . . . . . . . . . . . . . 23810.8 The Quantum Correspondence Principle . . . . . . . . . . . . 24210.8.1 Recovering the everyday world . . . . . . . . . . . . . . 24210.8.2 The Bohr Correspondence Principle . . . . . . . . . . . 24310.9 The Time Dependent Schrodinger equation . . . . . . . . . . . 24410.9.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . 24611 The Hydrogen Atom 24911.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 24911.2 Newtonian (Classical) Dynamics . . . . . . . . . . . . . . . . . 24911.3 The Bohr Atom . . . . . . . . . . . . . . . . . . . . . . . . . . 25111.4 Semi-classical spectrum from the Bohr correspondence principle25411.5 Emission and Absorption Spectra . . . . . . . . . . . . . . . . 25411.6 Three Dimensional Hydrogen Atom . . . . . . . . . . . . . . . 25611.6.1 Schrodinger Equation . . . . . . . . . . . . . . . . . . . 25611.6.2 Solutions and Quantum Numbers . . . . . . . . . . . . 25811.6.3 Fermions and the spin quantum number . . . . . . . . 26211.7 Periodic Table . . . . . . . . . . . . . . . . . . . . . . . . . . . 26511.7.1 Hydrogen-like atoms . . . . . . . . . . . . . . . . . . . 26511.7.2 Chemical Properties and the Periodic Table . . . . . . 26612 Nuclear Physics 27012.1 Properties of the Nucleus . . . . . . . . . . . . . . . . . . . . . 27012.1.1 Mass of Nucleons . . . . . . . . . . . . . . . . . . . . . 27012.1.2 Structure of Nucleus . . . . . . . . . . . . . . . . . . . 27112.1.3 The Nuclear Force . . . . . . . . . . . . . . . . . . . . 27112.2 Binding Energy and Stability . . . . . . . . . . . . . . . . . . 27412.2.1 Isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . 27412.2.2 Binding Energy . . . . . . . . . . . . . . . . . . . . . . 27512.2.3 Binding Energy per Nucleon . . . . . . . . . . . . . . . 27512.3 Formation of Elements: A Brief History of the Universe . . . . 27612.4 Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 27912.4.1 Unstable Isotopes . . . . . . . . . . . . . . . . . . . . . 27912.4.2 Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . 28112.4.3 Beta decay . . . . . . . . . . . . . . . . . . . . . . . . . 28212.4.4 Alpha Decay . . . . . . . . . . . . . . . . . . . . . . . 28312.4.5 Decay Rates . . . . . . . . . . . . . . . . . . . . . . . . 28312.4.6 Carbon Dating . . . . . . . . . . . . . . . . . . . . . . 28513 Supplementary: Advanced Topics 28713.1 Quantum Information and Quantum Computation . . . . . . . 28713.2 Relativity and quantum mechanics . . . . . . . . . . . . . . . 28714 Conclusions 28815 Appendix: Mathematical Background 28915.1 Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . . 28915.2 Probabilities and expectation values . . . . . . . . . . . . . . . 29115.2.1 Discrete Distributions . . . . . . . . . . . . . . . . . . 29115.2.2 Continuous probability distributions . . . . . . . . . . 29215.2.3 Dirac Delta Function . . . . . . . . . . . . . . . . . . . 29615.3 Supplementary: Fourier Series and Transforms . . . . . . . . . 29815.3.1 Fourier series . . . . . . . . . . . . . . . . . . . . . . . 29815.3.2 Fourier Transforms . . . . . . . . . . . . . . . . . . . . 30015.3.3 The mathematical uncertainty principle . . . . . . . . . 30215.3.4 Dirac Delta Function Revisited . . . . . . . . . . . . . 30315.3.5 Parseval's Theorem . . . . . . . . . . . . . . . . . . . . 30315.4 Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30415.4.1 Moving pure waves . . . . . . . . . . . . . . . . . . . . 30415.4.2 Complex Waves . . . . . . . . . . . . . . . . . . . . . . 30515.4.3 Group velocity and phase velocity . . . . . . . . . . . 30515.4.4 Wave packets . . . . . . . . . . . . . . . . . . . . . . . 30715.4.5 Wave number and momentum . . . . . . . . . . . . . . 30915.5 Derivation of Hydrogen Wave Functions . . . . . . . . . . . . 312

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Book SynopsisThis book offers an introduction to statistical mechanics, special relativity, and quantum physics. It is based on the lecture notes prepared for the one-semester course of "Quantum Physics" belonging to the Bachelor of Science in Material Sciences at the University of Padova.The first chapter briefly reviews the ideas of classical statistical mechanics introduced by James Clerk Maxwell, Ludwig Boltzmann, Willard Gibbs, and others. The second chapter is devoted to the special relativity of Albert Einstein. In the third chapter, it is historically analyzed the quantization of light due to Max Planck and Albert Einstein, while the fourth chapter discusses the Niels Bohr quantization of the energy levels and the electromagnetic transitions. The fifth chapter investigates the Schrodinger equation, which was obtained by Erwin Schrodinger from the idea of Louis De Broglie to associate to each particle a quantum wavelength. Chapter Six describes the basic axioms of quantum mechanics, which were formulated in the seminal books of Paul Dirac and John von Neumann. In chapter seven, there are several important application of quantum mechanics: the quantum particle in a box, the quantum particle in the harmonic potential, the quantum tunneling, the stationary perturbation theory, and the time-dependent perturbation theory. Chapter Eight is devoted to the study of quantum atomic physics with special emphasis on the spin of the electron, which needs the Dirac equation for a rigorous theoretical justification. In the ninth chapter, it is explained the quantum mechanics of many identical particles at zero temperature, while in Chapter Ten the discussion is extended to many quantum particles at finite temperature by introducing and using the quantum statistical mechanics. The four appendices on Dirac delta function, complex numbers, Fourier transform, and differential equations are a useful mathematical aid for the reader.Table of ContentsTable of Contents1 Classical Statistical Mechanics1.1 Kinetic Theory of Gases 1.1.1 Maxwell Distribution of Velocities1.1.2 Maxwell-Boltzmann Distribution of Energies 1.1.3 Single-Particle Density of States 1.2 Statistical Ensembles of Gibbs 1.2.1 Microcanonical Ensemble 1.2.2 Canonical Ensemble 1.2.3 Grand Canonical Ensemble 1.2.4 Many-Particle Density of States 2 Special Relativity 2.1 Lorentz Transformations 2.2 Einstein Postulates 2.2.1 Gedanken Experiment of Einstein 2.3 Relativistic Mechanics 2.3.1 Relativistic Kinematics 2.3.2 Relativistic Dynamics 3 Quantum Properties of Light 3.1 Black-Body Radiation 3.1.1 Ideal Black Body 3.1.2 Derivation of the Planck Law 3.2 Photoelectric E ect 3.2.1 Experimental Data 3.2.2 Theoretical Explanation 3.3 Energy and Linear Momentum of a Photon 3.4 Compton E ect 3.4.1 Theoretical Explanation 4 Quantum Energy Levels of Atoms 4.1 Energy Spectra 4.1.1 Energy Spectrum of Hydrogen Atom 4.2 Hydrogen Atom of Bohr4.2.1 Derivation of the Bohr Results 4.3 Energy Levels and Photons 4.4 Electromagnetic Transitions 5 Wave Properties of Matter 5.1 De Broglie Wavelength 5.1.1 Explaining the Bohr Quantization 5.2 Experiment of Davisson and Germer 5.3 Double-Slit Experiment with Light5.4 Double-Slit Experiment with Electrons 5.5 Old Quantum Mechanics of Bohr, Wilson and Sommerfeld5.6 Matrix Quantum Mechanics of Heisenberg, Born and Jordan 5.7 Wave Quantum Mechanics of Schrodinger 5.7.1 Derivation of the Schr odinger Equation 5.8 Formal Quantization Rules5.8.1 Schrodinger Equation for a Free Particle 5.8.2 Schrodinger Equation for a Particle in an External Potential 5.9 Stationary Schr odinger Equation6 Axioms of Quantum Mechanics 6.1 Matrix Mechanics 6.2 Axioms of Quantum Mechanics7 Applications of Quantum Mechanics 7.1 Quantum Particle in a One-Dimensional Box Potential7.2 Quantum Particle in a One-Dimensional Harmonic Potential8 Quantum Physics of Atoms 8.1 Quantum Particle in a Separable Potential 8.1.1 Quantum Particle in the Harmonic Potential 8.2 Dirac Notation for a Quantum State8.3 Electron in the Hydrogen Atom 8.3.1 Schrodinger Equation in Spherical Polar Coordinates 8.3.2 Selection Rules 8.4 Pauli Exclusion Principle and the Spin8.5 Semi-Integer and Integer Spin: Fermions and Bosons8.6 The Dirac Equation 8.6.1 The Pauli Equation and the Spin8.6.2 Dirac Equation with a Central Potential 8.6.3 Relativistic Hydrogen Atom and Fine Splitting 8.6.4 Relativistic Corrections to the Schrodinger Hamiltonian9 Quantum Mechanics of Many-Body Systems 9.1 Identical Quantum Particles 9.1.1 Spin-Statistics Theorem9.2 Non-Interacting Identical Particles9.2.1 Atomic Shell Structure and the Periodic Table of the Elements 9.3 Interacting Identical Particles9.3.1 Variational Principle9.3.2 Electrons in Atoms and Molecules10 Quantum Statistical Mechanics 10.1 Quantum Statistical Ensembles 10.1.1 Quantum Microcanonical Ensemble 10.1.2 Quantum Canonical Ensemble 10.1.3 Quantum Grand Canonical Ensemble 10.2 Bosons and Fermions at Finite Temperature 10.2.1 Gas of Photons at Thermal Equlibrium10.2.2 Gas of Massive Bosons at Thermal Equlibrium 10.2.3 Gas of Non-Interacting Fermions at Zero TemperatureAppendix A Dirac Delta Function A.1 The Heaviside Step Function A.2 The Strange Function of Dirac A.2.1 Dirac Function and the Integrals A.3 Dirac Function in D Spatial Dimensions Appendix B Complex Numbers B.1 Set of Complex Numbers B.2 Gauss Plane B.2.1 Polar Representation B.3 Euler Formula B.3.1 Proof of the Euler Formula B.3.2 De Moivre FormulaB.4 Fundamental Theorem of Algebra B.5 Complex Functions Appendix C Fourier Transform C.1 Geometric and Taylor SeriesC.2 Fourier Series .C.2.1 Complex Representation of the Fourier Series C.3 Fourier Integral C.3.1 Properties of the Fourier Transform C.3.2 Fourier Transform and Uncertanty TheoremC.4 Fourier Transform of Space-Time FunctionsAppendix D Di erential equations D.1 First-Order Ordinary Di erential EquationsD.1.1 Separation of Variables D.2 Second-Order Ordinary Di erential Equations D.3 Newton Law as a Second-Order ODE D.4 Partial Di erential Equations D.4.1 Wave Equation D.4.2 Di usion Equation Bibliography

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Book SynopsisThe aim of this textbook is to present in a comprehensive way several advanced topics of general relativity, including gravitational waves, tests of general relativity, time delay, spinors in curved spacetime, Hawking radiation, and geodetic precession to mention a few. These are all important topics in today's research activities from both a theoretical and experimental point of view. This textbook is designed for advanced undergraduate and graduate students to strengthen the knowledge acquired during the core courses on General Relativity. The author developed the book from a series of yearly lectures with the intention of offering a gentle introduction to the field. This book helps understanding the more specialized literature and can be used as a first reading to get quickly into the field when starting research. Chapter-end exercises complete the learning material to master key concepts.Trade Review“It is not a textbook, but rather a compendium of, as the title says, applications of General Relativity (GR) … useful for someone who knows the material but wants to look something up, refresh their memory, etc. … The breadth of topics covered is thus smaller than in some other books, but the depth is great. … it is very specialized, but fills an interesting niche.” (Phillip Helbig, The Observatory, Vol. 142 (1291), December, 2022)Table of ContentsIntroduction.- Elements of General Relativity.- Gravitational Waves.- Black Holes.- Tests of General Relativity.- Solutions.

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Book SynopsisThis book discusses theoretical predictions and their comparison with experiments of extended and modified classical and quantum theories of gravity. The goal is to provide a readable access and broad overview over different approaches to the topic to graduate and PhD students as well as to young researchers. The book presents both, theoretical and experimental insights and is structured in three parts. The first addresses the theoretical models beyond special and general relativity such as string theory, Poincare gauge theory and teleparallelism as well as Finsler gravity. In turn, the second part is focused on the observational effects that these models generate, accounting for tests and comparisons which can be made on all possible scales: from the universe as a whole via binary systems, stars, black holes, satellite experiments, down to laboratory experiments at micrometer and smaller scales. The last part of this book is dedicated to quantum systems and gravity, showing tests of classical gravity with quantum systems, and coupling of quantum matter and gravity.Table of ContentsPart 1: Theoretical Models beyond special and general relativity Section 1: Aspects of Lorentz invariance violations (Authors: Nick Mavromatos, Luci Menendez-Pidal De Cristina) Section 2: Deformed relativistic symmetry principles (Authors: Giulia Gubitosi, Michele Arzano, Javier Relancio) Section 3: Modified gravity - Poincare gauge theory and teleparallelism (Authors: Yuri Obukhov, Manuel Hohmann) Section 4: Aspects of Finsler gravity and modified dispersion relations in theory and observation (Authors: Volker Perlick, Jean-Francois Gliecenstein) Part 2: Observational effects beyond special and general relativity Section 1: Cosmic searches for Lorentz invariance violations (Authors: Tomislav Terzic, Carloes de los Heros) Section 2: Compact Objects (Authors: Jutta Kunz, Elisa Maggio, Yakov Shnir, Carlos Herdeiro, Aneta Wojnar) Section 3: Testing classical gravity (Authors: Eva Hackmann, Lijing Shao, Sven Herrmann) Section 4: Testing gravity and the standard model at short distance: The Casimir effect (Authors: Galina L. Klimchitskaya, Vladimir Mostepanenko)Part 3: Quantum Systems and Gravity Section 1: Testing Classical Gravity with Quantum Systems (Authors: Sven Herrmann) Section 2: Quantum Gravity in the Lab (Authors: Dennis Raetzel, Annupam Mazumdar, Hendrik Ulbricht) Section 3: Coupling Quantum Matter and Gravity (Authors: Andre Grossardt, Jan-Willem van Holten, Philip Schwartz , Domenico Giulini)

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Book Synopsis. The main aim of this book is to shine a spotlight on key experiments and their crucial importance for advancing our understanding of physics. Physics is an empirical science, and experiments have always been a driving force in the development of our understanding of nature. Facts matter. In that sense, the book attempts to be complementary to the many popularizations of theoretical physics, and to counterbalance the frequent emphasis there on more speculative ideas.Experimental physics is also an essential pillar in physics teaching, as well as helping broader audiences to better understand important concepts, particularly in challenging fields such as relativity or quantum physics, where our common sense intuition often fails.Readers are taken on an historical journey, starting with “Free Fall” and culminating in “Spooky Action at a Distance”. En route they will encounter many important branches of physics, whose main ideas and theoretical description will be given a more empirical meaning. At the end, the reader is invited to reflect on what could be exciting and important directions for fundamental physics. All readers with an undergraduate degree in physical sciences or engineering will enjoy and learn much from this stimulating and original text.Table of Contents1 The Winners Are . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Free Fall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1 Equality of Gravitational and Inertial Mass . . . . . . . . . . . . . . . . . . . . . 82.2 Galileo’s Experiments on Free Fall . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Newton’s Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.1 Looking up at the Sky . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.2 Newton’s Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.4 Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 Electromagnetic and Optical Unification . . . . . . . . . . . . . . . . . . . . . . . . . . 213.1 Electromagnetic Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2 Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.3 The Field Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.4 Electromagnetic Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.5 Unification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 Looking at Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.1 Natural Philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.2 Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.3 Limit theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.4 Brownian Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.4.1 The Random Walk as a Diffusion Model . . . . . . . . . . . . . . . . . 394.4.2 Sutherland–Einstein Relation . . . . . . . . . . . . . . . . . . . . . . . . . . 414.5 Perrin’s Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.6 Fluctuation–Dissipation Relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.1 Standard Hydrogen Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.2 Black Body Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525.3 Photoelectric Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54xixii Contents5.4 Compton Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585.5 Specific Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605.6 Spin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636 Wave-like Nature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 676.1 Early light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696.1.1 Young’s Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696.1.2 On the French side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716.1.3 Interacting Newton Bullets? . . . . . . . . . . . . . . . . . . . . . . . . . . . 736.2 X-rays and Bragg Scattering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 746.3 Davisson–Germer Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 766.4 Wavy Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 807 Finding Structure: Scattering and Fission . . . . . . . . . . . . . . . . . . . . . . . . . 857.1 Light Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 857.2 Particle Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 887.2.1 Geiger–Marsden–Rutherford Scattering . . . . . . . . . . . . . . . . . . 887.2.2 Standard Model Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 937.3 Nuclear Chain Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 948 Light in the Universe and the Invariance of Proper Time . . . . . . . . . . . 978.1 Michelson–Morley Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 988.2 Special Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1018.2.1 Popular Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1028.2.2 Minkowski Spacetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1038.2.3 Twin Paradox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1058.2.4 NonEuclidean Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1068.3 And More Generally . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1069 Dynamical Activity of the Vacuum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1099.1 Beginnings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1109.2 Lamb Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1129.2.1 Lamb–Retherford Experiment. . . . . . . . . . . . . . . . . . . . . . . . . . 1129.2.2 Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1159.3 Fluctuation Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1169.4 Casimir Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1179.5 Frenesy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11810 Phase Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12110.1 The Dream of Anaximenes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12310.2 Percolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12410.3 Criticality and Universality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12710.4 Superconductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13110.5 Superfluidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13210.6 Bose–Einstein Condensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133Contents xiii11 Nonlocality: Spooky Action at a Distance . . . . . . . . . . . . . . . . . . . . . . . . . 13511.1 About Alice, Living Far away from Bob . . . . . . . . . . . . . . . . . . . . . . . . 13711.2 Einstein’s Boxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13911.3 Einstein–Podolsky–Rosen Argument . . . . . . . . . . . . . . . . . . . . . . . . . . 14011.4 Bell’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14211.5 Bell Test Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14412 Future Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14712.1 Around 2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14812.1.1 The Statistical Mechanics of Geometry . . . . . . . . . . . . . . . . . . 15112.1.2 Relativity versus Quantum Mechanics . . . . . . . . . . . . . . . . . . . 15212.1.3 Quantum Statistical Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . 15312.2 Into the next hundred years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15512.2.1 Computational and Neuro(nal) Physics . . . . . . . . . . . . . . . . . . 15512.2.2 Physics of Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15712.2.3 Many-Body Nonequilibrium Physics . . . . . . . . . . . . . . . . . . . . 15912.2.4 Climate and Planetary Sciences . . . . . . . . . . . . . . . . . . . . . . . . 160References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

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Book SynopsisThis book offers an essential bridge between college-level introductions and advanced graduate-level books on special relativity. It begins at an elementary level, presenting and discussing the basic concepts normally covered in college-level works, including the Lorentz transformation. Subsequent chapters introduce the four-dimensional worldview implied by the Lorentz transformations, mixing time and space coordinates, before continuing on to the formalism of tensors, a topic usually avoided in lower-level courses. The book’s second half addresses a number of essential points, including the concept of causality; the equivalence between mass and energy, including applications; relativistic optics; and measurements and matter in Minkowski space-time. The closing chapters focus on the energy-momentum tensor of a continuous distribution of mass-energy and its co-variant conservation; angular momentum; a discussion of the scalar field of perfect fluids and the Maxwell field; and general coordinates.Every chapter is supplemented by a section with numerous exercises, allowing readers to practice the theory. These exercises constitute an essential part of the textbook, and the solutions to approximately half of them are provided in the appendix.Trade ReviewFrom the reviews:“The book is one of the best texts in special relativity designed for readers between the college-level and advanced level. … A number of useful and new examples is added at the end of every chapter of the book. … A very useful table of constants is added at the end of the book. … The book represents one of the best conspects in special relativity and is useful for professors of special relativity. It is good for students and every other reader.” (Alex Gaina, zbMATH, Vol. 1277, 2014)Table of ContentsFundamentals of Special Relativity.- Introduction.- The Principle of Relativity.- Groups—the Galilei group.- Galileian law of addition of velocities.- The lesson from electromagnetism.- The postulates of Special Relativity.- Consequences of the postulates.- Conclusion.- Problems.- The Lorentz transformation.- Introduction.- The Lorentz transformation.- Derivation of the Lorentz transformation.- Mathematical properties of the Lorentz transformation.- Absolute speed limit and causality.- Length contraction from the Lorentz transformation.- Time dilation from the Lorentz transformation.- Transformation of velocities and accelerations in Special Relativity.- Matrix representation of the Lorentz transformation.- The Lorentz group.- The Lorentz transformation as a rotation by an imaginary angle with imaginary time.- The GPS system.- Conclusion.- Problems.- The 4-dimensional world view.- Introduction.- The 4-dimensional world.- Spacetime diagrams.- Conclusion.- Problems.- The formalism of tensors.- Introduction.- Vectors and tensors.- Contravariant and covariant vectors.- Contravariant and covariant tensors.- Tensor algebra.- Tensor fields.- Index-free description of tensors.- The metric tensor.- The Levi-Civita symbol and tensor densities.- Conclusion.- Problems.- Tensors in Minkowski spacetime.- Introduction.- Vectors and tensors in Minkowski spacetime.- The Minkowski metric.- Scalar product and length of a vector in Minkowski spacetime.- Raising and lowering tensor indices.- Causal nature of 4-vectors.- Hypersurfaces.- Gauss’ theorem.- Conclusion.- Problems.- Relativistic mechanics.- Introduction.- Relativistic dynamics of massive particles.- The relativistic force.- Angular momentum of a particle.- Particle systems.- Conservation of mass-energy.- Conclusion.- Problems.- Relativistic optics.- Introduction.- Relativistic optics: null rays.- The drag effect.- The Doppler effect.- Aberration.- Relativistic beaming.- Visual appearance of extended objects.- Conclusion.- Problems.- Measurements in Minkowski spacetime.- Introduction.- Energy of a particle measured by an observer.- Frequency measured by an observer.- A more systematic treatment of measurement.- The 3+1 splitting.- Conclusion.- Problems.- Matter in Minkowski spacetime.- Introduction.- The energy-momentum tensor.- Covariant conservation.- Energy conditions.- Angular momentum.- Perfect fluids.- The scalar field.- The electromagnetic field.- Conclusion.- Problems.- Special Relativity in arbitrary coordinates.- Introduction.- The covariant derivative.- Spacetime curves and covariant derivative.- Physics in Minkowski spacetime revisited.- Conclusions.- Problems.- Solutions to selected problems.- References.- Index.

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Book SynopsisBeginning with an overview of the theory of black holes by the editor, this book presents a collection of ten chapters by leading physicists dealing with the variety of quantum mechanical and quantum gravitational effects pertinent to black holes. The contributions address topics such as Hawking radiation, the thermodynamics of black holes, the information paradox and firewalls, Monsters, primordial black holes, self-gravitating Bose-Einstein condensates, the formation of small black holes in high energetic collisions of particles, minimal length effects in black holes and small black holes at the Large Hadron Collider. Viewed as a whole the collection provides stimulating reading for researchers and graduate students seeking a summary of the quantum features of black holes.Table of ContentsFundamental Physics with Black Holes (Xavier Calmet).- Black holes and thermodynamics - The first half century (Daniel Grumiller, Robert McNees and Jakob Salzer).- The Firewall Phenomenon (R. B. Mann).- Monsters, Black holes and Entropy (Stephen D. H. Hsu).- Primordial Black Holes: sirens of the early Universe (Anne M. Green).- Self-gravitating Bose-Einstein condensates (Pierre-Henri Chavanis).- Quantum Amplitudes in Black-Hole Evaporation with Local Supersymmetry (P.D.D'Eath and A.N.St.J.Farley).- Hawking radiation from higher-dimensional black holes (Panagiota Kanti and Elizabeth Winstanley).- Black Holes at the Large Hadron Collider (Greg Landsberg).- Minimum length effects in black hole physics (Roberto Casadio, Octavian Micu, Piero Nicolini).

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Book SynopsisIn this compendium of essays, some of the world’s leading thinkers discuss their conceptions of space and time, as viewed through the lens of their own discipline. With an epilogue on the limits of human understanding, this volume hosts contributions from six or more diverse fields. It presumes only rudimentary background knowledge on the part of the reader.Time and again, through the prism of intellect, humans have tried to diffract reality into various distinct, yet seamless, atomic, yet holistic, independent, yet interrelated disciplines and have attempted to study it contextually. Philosophers debate the paradoxes, or engage in meditations, dialogues and reflections on the content and nature of space and time. Physicists, too, have been trying to mold space and time to fit their notions concerning micro- and macro-worlds. Mathematicians focus on the abstract aspects of space, time and measurement. While cognitive scientists ponder over the perceptual and experiential facets of our consciousness of space and time, computer scientists theoretically and practically try to optimize the space-time complexities in storing and retrieving data/information. The list is never-ending. Linguists, logicians, artists, evolutionary biologists, geographers etc., all are trying to weave a web of understanding around the same duo. However, our endeavour into a world of such endless imagination is restrained by intellectual dilemmas such as: Can humans comprehend everything? Are there any limits? Can finite thought fathom infinity? We have sought far and wide among the best minds to furnish articles that provide an overview of the above topics. We hope that, through this journey, a symphony of patterns and tapestry of intuitions will emerge, providing the reader with insights into the questions: What is Space? What is Time?Chapter [15] of this book is available open access under a CC BY 4.0 license. Table of ContentsPhilosophy: Śrīharṣa on the Indefinability of Time by Jonathan Duquette and Krishnamurti Ramasubramanian.- Why Spacetime Has a Life of its Own by James Robert Brown.- From Time to Time by Nathan Salmon.- Relativity Theory may not have the last Word on the Nature of Time: Quantum Theory and Probabilism by Nicholas Maxwell.- Space as a Source and as an Object of Knowledge: The Transformation of the Concept of Space in the Post-Kantian Philosophy of Geometry by Francesca Biagioli.- Space, Time and (how they) Matter by Valia Allori.- The Phenomenology of Space and Time: Husserl, Sartre, Derrida by Hans Herlof Grelland.- Time and Space in Ancient India, Pre­-Philosophical Period by Michael Witzel and Nataliya Yanchevskaya.- Time in Physics and Time in Awareness by E. C. G. Sudarshan.- Physics: The Future’s Not Ours to See, by Tony Sudbury.- Nature’s Book Keeping System by Gerard ‘t Hooft.- An anomaly in space and time and the origin of dynamics by Joan A. Vaccaro.- Spacetime and Reality: Facing the Ultimate Judge by Vesselin Petkov.- Hermann Weyl’s Space-Time Geometry and its Impact on Theories of Fundamental Interactions by Norbert Straumann.- Space, Time, and Adynamical Explanation in the Relational Blockworld by W.M. Stuckey, Michael Silberstein, and Timothy McDevitt.- Matter, Space, Time, and Motion: A Unified Gravitational Perspective by C. S. Unnikrishnan.- Spacetime is Doomed by George Musser.- Mathematics: Geometry and Physical Space by Mary Leng.- The Geometry of Manifolds and the Perception of Space by Raymond O. Wells, Jr.- Topos Theoretic Approach to Space and Time by Goro C. Kato.- Paradox? The Mathematics of Space-Time and the Limits of Human Understanding by Paul Ernest.- General Relativity, Time, and Determinism by James Isenberg.- “Now” has an infinitesimal positive duration by Reuben Hersh.- The Fundamental Problem of Dynamics by Julian Barbour.- What’s wrong with the Platonic ideal of space and time? by Lorenzo Sadun.- Biology/Cognitive Science: Syntactic Space by Rajesh Kasturirangan.- Time measurement in living systems: Human understanding and health implications by L Abhilash and Vijay Kumar Sharma.- The cellular space-the space of life by Pier Luigi Luisi.- The consciousness of space, the space of consciousness by Mauro Bergonzi and Pier Luigi Luisi.- Time and Suffering (False metaphors, (de)synchronous times, and internal dynamics) by Norman Sieroka.- Evolutionary Time and the Creation of the Space of Life by Randall E. Auxier.- Computer Science: A computational mathematics view of space, time and complexity by David H. Bailey and Jonathan M. Borwein.- The Black Hole in Mathematics by A. K. Dewdney.- Gödel’s Ontological Dreams by Gary Mar.- ‘Photographing the Footsteps of Time’: Space and Time in Charles Babbage’s Calculating Engines by Doron Swade.- Gödel incompleteness and the empirical sciences by N. C. A. da Costa and F. A. Doria.- Miscellaneous: The Novel and the Map: Spatiotemporal Form and Discourse in Literary Cartography by Robert T. Tally Jr.- Time, Space, and the Human Geographies of Opportunity by Donald G. Janelle.- Losing Time and Space: Experiencing Immersion by Diana J. Reichenbach. <

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Book SynopsisThis book summarizes the recent progress in the physics and astrophysics of neutron stars and, most importantly, it identifies and develops effective strategies to explore, both theoretically and observationally, the many remaining open questions in the field. Because of its significance in the solution of many fundamental questions in nuclear physics, astrophysics and gravitational physics, the study of neutron stars has seen enormous progress over the last years and has been very successful in improving our understanding in these fascinating compact objects. The book addresses a wide spectrum of readers, from students to senior researchers. Thirteen chapters written by internationally renowned experts offer a thorough overview of the various facets of this interdisciplinary science, from neutron star formation in supernovae, pulsars, equations of state super dense matter, gravitational wave emission, to alternative theories of gravity. The book was initiated by the European Cooperation in Science and Technology (COST) Action MP1304 “Exploring fundamental physics with compact stars” (NewCompStar).Trade Review Table of Contents1. Neutron stars formation and Core Collapse Supernovae P. Cerda'-Duran (ES), TBD 2. Strongly magnetized pulsars: explosive events and evolution Gourgouliatos (UK), P. Esposito (NL) 3. Radio pulsars: testing gravity and detecting GWs D. Perrodin (IT), A. Sesana (UK) (TBC) 4. Accreting pulsars: mixing-up accretion phases in transitional systems Di Salvo (IT), S. Campana (IT) 5. Testing the EOS with electromagnetic observations N. Degenaar (UK), Juri Poutanen (FI) 6. Nuclear EOS for Compact Stars & Supernovae A. Fantina (FR), F. Burgio (I) 7. Low-energy QCD & Super-dense matter D. Blaschke (PL), C. Pethick (DK) 8. Superfluidity & Superconductivity in Compact Stars B. Haskell (PL), A. Sedrakian (D) 9. Transport phenomena & reactions rates for Compact Stars & Supernovae P. Shternin (RU), A. Schmitt (UK) 10. GW emission from merging BNSs T. Hinderer (D), L. Rezzolla (D) < 11. EM emission and nucleosynthesis from BNSs A. Arcones (D) B. Giacomazzo (I) 12. GW emission from single neutron stars L. Gualtieri (I), K. Glampedakis (ES) 13. Universal relations and Alternative Gravity Theories D. Doneva (BG), G. Pappas (PT)

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Book SynopsisIn diesem Buch wird der Versuch unternommen, Schülern der oberen Klassen und allen, die sich für Physik inter­ essieren, etwas über die Gravitation zu vermitteln. Durch die gravitative Wechselwirkung-die schwächste aller in der Natur bekannten Wechselwirkungen-wird die Bewegung der Himmelskörper, der Planeten, Sterne und Galaxien, sowie die Entwicklung des Universums als Ganzes bestimmt. Unter Laborbedingungen sind die gra­ vitativen Effekte jedoch so klein, daß es keine leichte Aufgabe ist, sie zu messen. Als die Autoren dieses Buch über die gravitative Wechselwirkung schrieben, bemühten sie sich, dem Aus­ spruch des sowjetischen Physikers I. Je. Tamm zu folgen: "Ein Student ist keine Gans, die man füllen, sondern eine Fackel, die man anzünden muß." Offensichtlich gilt das auch für Schüler (von denen ja einige später Studenten werden). Daher haben sich die Autoren folgende Aufgabe gestellt: Erstens wollen sie den Leser mit den modernen Vorstellungen über die gravitative Wechselwirkung be­ kannt machen. Zweitens wollen sie ihn empfinden lassen, wie die erstaunlichen Besonderheiten der Gravitation im Experiment zutage treten. In diesem Buch wird auch ein wenig über die histori­ sche Entwicklung der Ideen und Experimente berichtet.Table of Contents1. Über das physikalische Experiment im allgemeinen und über die Gravitationsexperimente im besonderen.- 2. Was wußte Newton über die Schwerkraft?.- 3. Die Relativität der Bewegung.- 4. Was besagt die Allgemeine Relativitätstheorie?.- 5. Welche Beobachtungshinweise liefert die Allgemeine Relativitätstheorie?.- 6. Das Meßpotential der Menschheit—gestern und heute.- 7. Wieviele Massesorten gibt es?.- 8. Wie entsteht die Rot- bzw. Violettverschiebung elektromagnetischer Wellen?.- 9. Die Sonne verzerrt das Bild der Metagalaxis und verzögert Radioechos.- 10. Inwiefern irrte Kepler?.- 11. Das Gravitationsfeld rotierender Körper.- 12. Wie kann man Gravitationswellen empfangen?.- 13. Wie „erkennt“ man ein Schwarzes Loch?.- 14. Die Gravitation am Rande der Metagalaxis.- 15. Ist die Gravitationskonstante wirklich konstant? (Über andere Gravitationstheorien).- Schlußwort.- Anhang: Welchen Nutzen besitzt die Gravimetrie, und gibt es Schwerelosigkeit auf der Umlaufbahn?.

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Book SynopsisBryce DeWitt, a student of Nobel Laureate Julian Schwinger, was himself one of the towering figures in 20th century physics, particularly renowned for his seminal contributions to quantum field theory, numerical relativity and quantum gravity. In late 1971 DeWitt gave a course on gravitation at Stanford University, leaving almost 400 pages of detailed handwritten notes. Written with clarity and authority, and edited by his former student Steven Christensen, these timeless lecture notes, containing material or expositions not found in any other textbooks, are a gem to be discovered or re-discovered by anyone seriously interested in the study of gravitational physics.Trade ReviewFrom the reviews:“DeWitt’s lectures cover interesting and detailed material which is rarely found in other text books. It is a book for the advanced reader.” (Norbert Dragon, General Relativity and Gravitation, Vol. 44, 2012)Table of ContentsReview of the Uses of Invariants in Special Relativity.- Accelerated Motion in Special Relativity.- Realization of Continuous Groups.- Riemannian Manifolds.- The Free Particle Geodesics.- Weak Field Approximation. Newton`s Theory.- Ensembles of Particles.- Production of Gravitational Fields by Matter.- Conservation Laws.- Phenomenological Description of a Conservative Continuous Medium.- Solubility of the Einstein and Matter Equations.- Energy, Momentum and Stress in the Gravitational Field.- Measurement of Asymptotic Field.- The Electromagnetic Field.- Gravitational Waves.- Spinning Bodies.- Weak Field Gravitational Wave.- Stationary Spherically (or Rotationally) Symmetric Metric.- Kerr Metric Subcalculations.- Friedmann Cosmology.- Dynamical Equations and Diffeomorphisms.

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Book SynopsisBlack Holes are still considered to be among the most mysterious and fascinating objects in our universe. Awaiting the era of gravitational astronomy, much progress in theoretical modeling and understanding of classical and quantum black holes has already been achieved. The present volume serves as a tutorial, high-level guided tour through the black-hole landscape: information paradox and blackhole thermodynamics, numerical simulations of black-hole formation and collisions, braneworld scenarios and stability of black holes with respect to perturbations are treated in great detail, as is their possible occurrence at the LHC. An outgrowth of a topical and tutorial summer school, this extensive set of carefully edited notes has been set up with the aim of constituting an advanced-level, multi-authored textbook which meets the needs of both postgraduate students and young researchers in the fields of modern cosmology, astrophysics and (quantum) field theory. Table of ContentsBlack Holes and their Properties.- What Exactly is the Information Paradox?.- Classical Yang–Mills Black Hole Hair in Anti-de Sitter Space.- Black Hole Thermodynamics and Statistical Mechanics.- Colliding Black Holes and Gravitational Waves.- Numerical Simulations of Black Hole Formation.- Higher-Dimensional Black Holes.- Black Holes in Higher-Dimensional Gravity.- Braneworld Black Holes.- Higher Order Gravity Theories and Their Black Hole Solutions.- Gravitational Waves from Braneworld Black Holes.- Black Holes at the Large Hadron Collider.- Perturbations of Black Holes.- Perturbations and Stability of Higher-Dimensional Black Holes.- Analytic Calculation of Quasi-Normal Modes.

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Book SynopsisThe Physics of the Early Universe is an edited and expanded version of the lectures given at a recent summer school of the same name. Its aim is to present an advanced multi-authored textbook that meets the needs of both postgraduate students and young researchers interested in, or already working on, problems in cosmology and general relativity, with emphasis on the early universe. A particularly strong feature of the present work is the constructive-critical approach to the present mainstream theories, the careful assessment of some alternative approaches, and the overall balance between theoretical and observational considerations. As such, this book will also benefit experienced scientists and nonspecialists from related areas of research. Trade ReviewFrom the reviews: "This is a set of 9 review articles given as part of a 2003 summer school on Syros Island, Greece. … this book provides a solid introduction to current research in early universe physics, which should be useful for PhD students or postdoctoral researchers who want the real thing. … This, then, is a useful book for someone wanting to leap right into modern theoretical ideas of early universe physics." (Douglas Scott, Classical and Quantum Gravity, Issue 24, 2007)Table of ContentsAn Introduction to the Physics of the Early Universe.- Cosmological Perturbation Theory.- Cosmic Microwave Backgrond Anisotropies.- Oberservational Cosmology.- Dark Matter and Dark Energy.- String Cosmology.- Brane-World Cosmology.- Gravitational Wave Astronomy: the High Frequency Window.- Computational Black Hole Dynamics.

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Book SynopsisThis book is aimed at theoretical as well as primarily physicists graduate students in field working quantum theory, quantum gravity, theories, gauge to sdme and and, it is not extent, general relativity cosmology. Although aimed at a I that it also be of level, hope in mathematically rigorous may terest to mathematical and mathematicians in physicists working spectral of differential mani geometry, spectral asymptotics on operators, analysis differential and mathematical methods in folds, geometry quantum theory. Thisbook will be considered too abstract some but certainly by physicists, not detailed and most mathematicians. This in completeenoughby means, thatthe material is at the level of particular, presented "physical" So, rigor. there theorems and areno and technicalcalculationsare lemmas, proofs long omitted. I tried detailed to a ofthe basic Instead, give presentation ideas, methodsandresults. Itried makethe to as andcom Also, exposition explicit as the lessabstractandhaveillustratedthe plete possible, methods language and results withsome As is well "onecannot examples. known, cover every in an text. The in this thing", especially introductory approach presented book the lines is a further of the so called along goes (and development) fieldmethod ofDe Witt. As a Ihavenot dealt at background consequence, allwithmanifoldswith boundary,non Laplacetype (ornonminimal) opera Riemann Cartan manifolds well with as as recent tors, developments many and advanced such Ashtekar's more as topics, approach,supergravity,strings, matrix etc. The membranes, interested reader is referred models, M theory tothe literature.Trade Review"This monograph rightly belongs to a series ‘Lecture notes in Physics’, as it represents a well-written review of main results by the author, who is a recognized expert on heat kernel techniques in quantum gravity. [...] The results exposed in this book reflect the major contributions of the author to differential geometry and the theory of differential operators. They have many applications in quantum field theory with background fields, and indeed, the book can be used as a text for a short graduate course in the heat kernel techniques and their quantum gravity." (Mathematical Reviews 2003a)Table of ContentsBackground Field Method in Quantum Field Theory.- Technique for Calculation of De Witt Coefficients.- Partial Summation of Schwinger-De Witt Expansion.- Higher-Derivative Quantum Gravity.- Conclusion.

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Book SynopsisThe idea to hold a workshop on globular clusters in Concepcion emerged during 2005 out of a variety of circumstances. Four years had passed since the IAUSymposium 207 onExtragalactic Globular Clusters inPuc' on, atime span, which we thought to be long enough for justifying a new meeting with theintent toreviewthemostrecentdevelopments inthe?eld of extragalactic stars clusters. Originally intended to be a small-scale workshop, the response from the community was overwhelming so that only a full-scale international conferencewas abletocopewith thenumerousrequestsfortalksandposters. Finally, about 160 participants gathered in Concepci' on on March 6th, 2006. The venue was the university lecture hall located in the facultad de - manidadesyartesoftheUniversidaddeConcepci' on.Posterswereexposedin the lobby of the faculty building. The weather was as good as one can reas- ablyexpectfromalatesummerinConcepci' on.Althoughtheprogrammewas so tight that separate poster sessions other than those during co?ee breaks could not be accomodated, posters received a lot of attention. From the ?rst to the last talk, the atmosphere was inspiring and the conference could keep its tension for ?ve full days. This clearly shows that the attraction which globular clusters exercise on astrophysicists of quite di?erent ?avours, is as strong as ever.Table of ContentsDetailed Studies of Individual Globular Clusters.- Detailed Chemical Abundances of Extragalactic Globular Clusters.- Spectroscopic Abundances and Radial Velocities of the Galactic Globular Clusters 2MASS GC01 and 2MASS GC02: Preliminary Results.- Abundance Anomalies in Galactic Globular Clusters – Looking for the Stellar Culprits.- Globular Clusters in the Direction of the Inner Galaxy.- Globular Cluster Research with Astronomical Archives.- Super-He-Rich Populations in Globular Clusters.- Testing the BH 176 and Berkeley 29 Association with GASS/Monoceros.- New Yonsei-Yale (Y 2) Isochrones and Horizontal-Branch Evolutionary Tracks with Helium Enhancements.- Search for Candle Stars in Globular Clusters: Spectroscopic Analysis of Post-AGB Candidates.- The Lack of Binaries Among Hot Horizontal Branch Stars: M80 and NGC5986.- Semi-Empirical Determination of the Mass Distribution of Horizontal Branch Stars in M3.- The Most Massive Clusters.- Globular Clusters, Galactic Nuclei and Supermassive Black Holes.- UCDs – A Mixed Bag of Objects.- Ultra-Compact Dwarf Galaxies and Globular Clusters: A Review of Their Spatial and Dynamical Properties.- The Maximum Mass of Star Clusters.- The Stellar Population of Ultra-Compact Dwarf Galaxies.- News on Ultra-Compact Dwarfs and Blue Globular Clusters.- UCDs and GCs: Structural Differences from HST Imaging.- Ultra-Compact Stellar Systems in the Fornax Galaxy Cluster.- Multi-Colour Imaging of Ultra-Compact Objects in the Fornax Cluster.- Young Star Clusters.- Hierarchical Formation of Galactic Clusters.- Young Massive Clusters – Formation Efficiencies and (Initial) Mass Functions.- The Radii of Thousands of Star Clusters in M51 with HST/ACS.- Extragalactic Star Clusters in Merging Galaxies.- The Environment of Young Massive Clusters.- Star/Cluster Formation in Complexes: Insights from IFUs and HST.- Spectral Evolution of Blue Concentrated Star Clusters in the Large Magellanic Cloud.- Young Star Clusters in the SMC.- Molecular Clouds and Star Formation in the Magellanic System by NANTEN.- Two Star Cluster Populations in NGC 45.- Characterization of Open Cluster Remnants.- HST Photometry of the Binary Globular Cluster Sersic 13N-S in NGC5128[1].- Globular Cluster Systems in Dwarf and Irregular Galaxies.- LMC Cluster Abundances and Kinematics.- Globular Clusters in Dwarf Galaxies.- Globular Clusters in Dwarf and Giant Galaxies.- The Age-Metallicity Relation of the SMC.- Integrated Spectroscopic Analysis of Galactic and Small Magellanic Cloud Clusters.- Variable Stars in the Globular Clusters and in the Field of the Fornax dSph Galaxy.- Physical Parameters of Intermediate-Age LMC Clusters from Modelling of HST CMDs.- RGB Properties of the LMC/SMC Clusters in the Infrared.- WLM-1: A Non-Rotating, Gravitationally Unperturbed, Highly Elliptical Extragalactic Globular Cluster.- Globular Cluster Systems in Spiral Galaxies.- Star Clusters in M33 – Clues to Galaxy Formation and Evolution.- M31 and its Globular Clusters.- IR Integrated Light Colors For Galactic GCs and An Update on Young M31 Globular Clusters.- Nuclear Star Clusters in Edge-on Galaxies.- HST ACS Wide-Field Photometry of the Sombrero Galaxy Globular Cluster System.- Intermediate-Age Globular Clusters in M31.- Metal-Poor Globular Clusters of the Galactic Bulge.- Globular Cluster System and Milky Way Properties Revisited.- RR Lyrae-Based Calibration of the Globular Cluster Luminosity Function.- Globular Cluster Systems in Spiral Galaxies Using ACS Imaging.- Laser Guide Star Imaging of M31 Globulars.- GALEX UV Observations of M31 Globular Clusters.- Integrated Spectroscopy of Galactic Globular Clusters.- Globular Cluster Systems in Early-Type Galaxies.- Globular Cluster Systems: Do They Really Trace Star Formation? (Or Rather: What Mode of Star Formation Do They Trace?).- Globular Clusters in Early Type Galaxies.- Globular Clusters and Galaxy Formation.- Globular Cluster Systems in Giant Ellipticals: New and Old Patterns.- The ACS Virgo Cluster Survey.- Globular Clusters at the Centre of the Fornax Cluster: Tracing Interactions Between Galaxies.- Globular Cluster Bimodality Revisited (and the Globulars-Galaxy Halo Connection).- Globular Cluster Systems, Diffuse Star Clusters, and Host Galaxies in the ACS Virgo Cluster Survey.- Hot Populations in M87 Globular Clusters.- A Subaru/Suprime-Cam Wide-Field Survey of Globular Cluster Populations around M87.- Stellar Populations of Globular Clusters in NGC 1407.- The Globular Cluster System of NGC 5846 Revisited: Colours, Sizes and X-Ray Counterparts.- Globular Cluster Systems in Shell Ellipticals.- GMOS Photometry of Five Globular Cluster Systems: NGC 4649, NGC 3923, NGC 524, NGC 3115 and NGC 3379.- Structural Parameters from Ground-based Observations of Globular Clusters in NGC 5128.- Globular Cluster Populations in Early-Type Galaxies.- The Low-Mass X-Ray Binary Globular Cluster Connection in the ACS Virgo Cluster Survey.- The Globular Cluster System of NGC 5128: Combining Broad-Band Color and Lick Index Analysis.- The Galaxy – Globular Cluster Connection in NGC 3115.- Velocity Dispersions of Bright Globular Clusters in NGC 5128.- Evolution of Cluster Systems and their Host Galaxies.- Imprint of Galaxy Formation and Evolution on Globular Cluster Properties.- Formation of Globular Clusters in Hierarchical Cosmology: ART and Science.- Globular Cluster Formation in Mergers.- The Formation Histories of Metal-Rich and Metal-Poor Globular Clusters.- Globular Cluster System Evolution in Early Type Galaxies.- Star Cluster Evolution: From Young Massive Star Clusters to Old Globulars.- A Wide-Field Survey of the Globular Cluster Systems of Giant Galaxies.- IGCs in the Virgo Cluster.- A New Explanation of Globular Cluster Color Distributions.- Formation of Intracluster and Intercluster Globular Clusters.- The Effect of Giant Molecular Clouds on Star Clusters.- Metal-rich Globular Clusters: An Unaccounted Factor Responsible for Their Formation?.- On the Globular Cluster Color Distributions.- Dynamical Evolution of Star Clusters.- Dissolution of Globular Clusters.- Dynamical Masses of Young Star Clusters: Constraints on the Stellar IMF and Star-Formation Efficiency.- Dynamical Evolution of Rotating Globular Clusters with Embedded Black Holes.- The Dynamical Evolution of Young Clusters and Galactic Implications.- Simulations of Globular Clusters Merging in Galactic Nuclear Regions.- The Origin of the Gaussian Initial Mass Function of Globular Cluster Systems.- Evolution of Globular Cluster Systems.- Tidal Disruption and the Tale of Three Clusters.- Tidal Tails Around Globular Clusters: Are they Good Tracers of Cluster Orbits?.- Modelling the Tidal Tails of NGC 5466.- The Search for Tidal Tails of Globular Clusters: NGC4147.- Internal Rotation of Young Globular Clusters.- Mass Segregation in Young Star Clusters.- Dynamics of Globular Cluster Systems.- Kinematics of Globular Cluster Systems.- Dark Matter in the Elliptical Galaxies NGC 1399 and NGC 4636.- Ages, Abundances, and Kinematics of Globular Clusters in NGC 3379 and NGC 4649 with Gemini/GMOS.- The Dark Halo of NGC 1399 and MOND.- Dynamics of the Globular Cluster System of NGC 5128.- Open Questions in the Globular Cluster – Galaxy Connection.- Open Questions in the Globular Cluster – Galaxy Connection.

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Book SynopsisThis book provides an original introduction to the geometry of Minkowski space-time. A hundred years after the space-time formulation of special relativity by Hermann Minkowski, it is shown that the kinematical consequences of special relativity are merely a manifestation of space-time geometry.The book is written with the intention of providing students (and teachers) of the first years of University courses with a tool which is easy to be applied and allows the solution of any problem of relativistic kinematics at the same time. The book treats in a rigorous way, but using a non-sophisticated mathematics, the Kinematics of Special Relativity. As an example, the famous "Twin Paradox" is completely solved for all kinds of motions.The novelty of the presentation in this book consists in the extensive use of hyperbolic numbers, the simplest extension of complex numbers, for a complete formalization of the kinematics in the Minkowski space-time.Moreover, from this formalization the understanding of gravity comes as a manifestation of curvature of space-time, suggesting new research fields.Table of ContentsIntroduction.- Hyperbolic Numbers.- Geometrical Representation of Hyperbolic Numbers.- Trigonometry in the Hyperbolic (Minkowski) Plane.- Equilateral Hyperbolas and Triangles in the Hyperbolic Plane.- The Motions in Minkowski Space-Time (Twin Paradox).- Some Final Considerations.

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Book SynopsisThis graduate-level, course-based text is devoted to the 3+1 formalism of general relativity, which also constitutes the theoretical foundations of numerical relativity. The book starts by establishing the mathematical background (differential geometry, hypersurfaces embedded in space-time, foliation of space-time by a family of space-like hypersurfaces), and then turns to the 3+1 decomposition of the Einstein equations, giving rise to the Cauchy problem with constraints, which constitutes the core of 3+1 formalism. The ADM Hamiltonian formulation of general relativity is also introduced at this stage. Finally, the decomposition of the matter and electromagnetic field equations is presented, focusing on the astrophysically relevant cases of a perfect fluid and a perfect conductor (ideal magnetohydrodynamics). The second part of the book introduces more advanced topics: the conformal transformation of the 3-metric on each hypersurface and the corresponding rewriting of the 3+1 Einstein equations, the Isenberg-Wilson-Mathews approximation to general relativity, global quantities associated with asymptotic flatness (ADM mass, linear and angular momentum) and with symmetries (Komar mass and angular momentum). In the last part, the initial data problem is studied, the choice of spacetime coordinates within the 3+1 framework is discussed and various schemes for the time integration of the 3+1 Einstein equations are reviewed. The prerequisites are those of a basic general relativity course with calculations and derivations presented in detail, making this text complete and self-contained. Numerical techniques are not covered in this book.Trade ReviewFrom the reviews:“The monograph originating from lectures is devoted to the 3+1 formalism in general relativity. It starts with three chapters on basic differential geometry, the geometry of single hypersurfaces embedded in space-time, and the foliation of space-time by a family of spacelike hypersurfaces. … With the attempt to make the text self-consistent and complete, the calculations are … detailed such that the book is well suitable for undergraduate and graduate students.” (Horst-Heino von Borzeszkowski, Zentralblatt MATH, Vol. 1254, 2013)“This book is written for advanced students and researchers who wish to learn the mathematical foundations of various approaches that have been proposed to solve initial value problems (with constraints) for the Einstein equations numerically. … Even for experts it may be useful, as it includes an extensive bibliography up to 2011.” (Hans-Peter Künzle, Mathematical Reviews, January, 2013)Table of ContentsBasic Differential Geometry.- Geometry of Hypersurfaces.- Geometry of Foliations.- 3+1 decomposition of Einstein Equation.- 3+1 Equations for Matter and Electromagnetic Field.- Conformal Decompositon.- Asymptotic Flatness and Global Quantities.- The Initial Data Problem.- Choice of Foliation and Spatial Coordiinates.- Evolution Schemes.- Conformal Killing Operator and Conformal Vector Laplacian.- Sage Codes.

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Book SynopsisThe Springer Handbook of Spacetime is dedicated to the ground-breaking paradigm shifts embodied in the two relativity theories, and describes in detail the profound reshaping of physical sciences they ushered in. It includes in a single volume chapters on foundations, on the underlying mathematics, on physical and astrophysical implications, experimental evidence and cosmological predictions, as well as chapters on efforts to unify general relativity and quantum physics. The Handbook can be used as a desk reference by researchers in a wide variety of fields, not only by specialists in relativity but also by researchers in related areas that either grew out of, or are deeply influenced by, the two relativity theories: cosmology, astronomy and astrophysics, high energy physics, quantum field theory, mathematics, and philosophy of science. It should also serve as a valuable resource for graduate students and young researchers entering these areas, and for instructors who teach courses on these subjects.The Handbook is divided into six parts. Part A: Introduction to Spacetime Structure. Part B: Foundational Issues. Part C: Spacetime Structure and Mathematics. Part D: Confronting Relativity theories with observations. Part E: General relativity and the universe. Part F: Spacetime beyond Einstein.Trade Review“This is a complete comprehensive textbook of all areas of classical and relativistic Physics including mechanics, E & M, quantum theory, perturbation, solid state, and particle physics. … It is good enough to be read cover to cover and will not disappoint the reader reviewer. I highly recommend this book for physics students, and investigators in physics theories.” (Joseph J. Grenier, Amazon.com, January, 2016)“This is a splendid and very comprehensive review of the special and general theories of relativity and their applications, in a collection of about 40 articles by experts in the field. … the book will appeal to a wide variety of readers, from advanced undergraduates to experts in the field. … I doubt that there is any physicist who would not find something new and interesting here.” (Alan Heavens, The Observatory, Vol. 135 (1245), April, 2015)Table of ContentsPreface (A. Ashtekar, V. Petkov).- Part A – Introduction to Spacetime Structure.- Chap. 1 From Aether Theory to Special Relativity.- Chap. 2 The Historical Origins of Spacetime.- Chap. 3 Relativity Today.- Chap. 4 Acceleration and Gravity: Einstein's Principle.- Chap. 5 The Geometry of Newton's and Einstein's Theories.- Part B – Foundational Issues.- Chap. 6 Time in Special Relativity.- Chap. 7 Rigid Motion and Adapted Frames.- Chap. 8 Physics as Spacetime Geometry.- Chap. 9 Electrodynamics of Radiating Charges.- Chap. 10 The Nature and Origin of Time-Asymmetric Spacetime Structures.- Chap. 11 Teleparallelism: A new Insight into Gravity.- Chap. 12 Gravity and the Spacetime: An Emergent Perspective.- Chap. 13 Spacetime and the Passage of Time.- Part C – Spacetime Structure and Mathematics.- Chap. 14 Unitary Representations of the Inhomogeneous Lorentz Group and Their Significance in Quantum Physics.- Chap. 15 Spinors.- Chap. 16 The Initial Value Problem in General Relativity.- Chap. 17 Dynamical and Hamiltonian Formulation of General Relativity.- Chap. 18 Positive Energy Theorems in General Relativity.- Chap. 19 Conserved Charges in Asymptotically (Locally) AdS Spacetimes.- Chap. 20 Spacetime Singularities.- Chap. 21 Singularities in Cosmological Spacetimes.- Part D – Confronting Relativity theories with observations.- Chap. 22 The experimental status of Special and General Relativity Chap. 23. Observational Constraints on Local Lorentz Invariance.- Chap. 24 Relativity in GNSS.- Chap. 25 Quasi Local Black Hole Horizons.- Chap. 26 Gravitational Astronomy.- Chap. 27 Probing Dynamical Spacetimes with Gravitational Waves.- Part E – General Relativity and the Universe.- Chap. 28 Einstein's Equation, Cosmology and Astrophysics.- Chap. 29 Viscous Universe Models.- Chap. 30 Friedmann-Lemaitre-Robertson-Walker Cosmology.- Chap. 31 Exact Approach to Inflationary Universe Models.- Chap. 32 Cosmology with the Cosmic Microwave Background.- Part F – Spacetime Beyond Einstein.- Chap. 33 Quantum Gravity.- Chap. 34 Quantum Gravity via Causal Dynamical Triangulations.- Chap. 35 String Theory and Primordial Cosmology.- Chap. 36 Quantum Spacetime.- Chap. 37 Gravity, Geometry and the Quantum.- Chap. 38 Spin Foams.- Chap. 39 Loop Quantum Cosmology.- Acknowledgements.- About the Authors.- Subject Index.

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Book SynopsisDer bekannte Astronom Karl Schwarzschild (1873-1916) gilt als der Begr}nder der Astrophysik und als hervorragender Forscher mit einer erstaunlichen Bandbreite seiner Interessen. Arbeiten zur Himmelsmechanik, Elektrodynamik und Relativit{tstheorie weisen ihn als vorz}glichen Mathematiker und Physiker seiner Zeit aus. Untersuchungen zur Photographischen Photometrie, Optik und Spektroskopie zeigen den versierten Beobachter, der sein Me~instrument beherrscht. Schlie~lich arbeitete Schwarzschild als Astrophysiker und an Sternatmosph{ren, Kometen, Struktur und Dynamikvon Sternsystemen. Die in seinem kurzen Leben entstandene F}lle von wissenschafltichen Arbeiten ist in drei B{nden der Gesamtausgabe gesammelt, erg{nzt durch biographisches Material und ein Essay des Nobelpreistr{gers S. Chandrasekhar und Annotationen von Fachleuten in jedem der drei B{nde.Table of Contents5. Astronomical Positioning.- 5.1 Ueber photographische Ortsbestimmung / On Photographic Position Determination.- 5.2 Über photographische Breitenbestimmung mit Hilfe eines hängenden Zenitkollimators / On Determining Latitude Using a Suspended Zenith Collimator.- 5.3 Über Breitenbestimmung mit Hilfe einer hängenden Zenitkamera / On Latitude Determination Using a Suspended Zenith Camera.- 5.4 Bestimmung der Polhöhe von Göttingen u. der Deklinationen von 375 Zenithsternen mit der hängenden Zenithkamera / Determination of the Altitude of the Pole at Göttingen and the Declination of 375 Zenith Stars Using the Suspended Zenith Camera (with W. Dziewulski).- 5.5 Über einen Transformator zur Auflösung sphärischer Dreiecke, besonders für Zwecke der Ortsbestimmung im Luftballon / On a Transformer for the Solution of Spherical Triangles, Especially for Position Determination in Air Balloons.- 5.6 Tafeln zur astronomischen Ortsbestimmung im Luftballon bei Nacht, sowie zur leichten Bestimmung der mitteleuropäischen Zeit an jedem Orte Deutschlands / Tables for Astronomical Position Determination in Air Balloons at Night and for Easy Determination of Central-European Time at any Point in Germany (with o. Birck).- 5.7 Künstlicher Horizont and Ballonsextant / Artificial Horizon and Balloon Sextant.- 5.8 Libellenhorizont und Libellensextant / Bubble Horizon and Bubble Sextant.- 6. Photographie Photometry.- 6.1 Die Bestimmung von Sternhelligkeiten aus extrafocalen photographischen Aufnahmen / The Determination of Stellar Magnitudes from Extrafocal Exposures.- 6.2 Beiträge zur photo graphischen Photometrie der Gestirne / Contributions on the Photographic Photometry of Stars.- 6.3 Ueber Abweichungen vom Reciprocitätsgesetz für Bromsilbergelatine / On Departures from the Reciprocity Law for Silver-Bromide Gelatine.- 6.4 Ueber die Wirkung intermittirender Belichtung auf Bromsilbergelatine / On the Effects of Intermittent Exposures on Silver-Bromide Gelatine.- 6.5 Bemerkungen zur Sensitometrie / Remarks on Sensitometry.- 6.6 über die photographische Vergleichung der Helligkeit verschiedenfarbiger Sterne / On the Photographic Comparison of the Magnitudes of Stars of Different Colours.- 6.7 Ueber sensitometrische Regeln und ihre astronomische Anwendung / On Sensitometry Laws and Their Astronomical Application.- 6.8 Professor G. Jägers Theorie des photographischen Prozesses / Professor G. Jäger’sf Theory of the Photographic Process.- 6.9 Plan zur Durchführung einer photographisch-photometrischen Durchmusterung des nördlichen Himmels / Plan for Carrying Out a Photographic-Photometric Survey of the Northern Sky.- 6.10 Über eine Schraffierkassette zur Aktinometrie der Sterne / On a Schraffierkassette for Stellar Actinometry (with Br. Meyermann).- 6.11 Über eine Interpolationsaufgabe der Aktinometrie / On an Interpolation Problem in Actinometry.- 6.12 Aufnahmen des Sternhaufens h Persei mit Spiegeln von sehr großem öffnungsverhältnis / Exposures of the Cluster h Persei Using Mirrors with Very Large Aperture Ratios (with W. Villiger).- 6.13 Über eine neue Schraffierkassette / On a New Schraffierkassette (with Br. Meyermann).- 6.14 Über die Farbentönung der Sterne / On the Colour Tints of the Stars.- 6.15 Remarque sur la determination des grandeurs photographiques absolues / Note on the Determination of Absolute Photographic Magnitudes.- 6.16 Über die Bestimmung absoluter photographischer Helligkeiten / On the Determination of Absolute Photographic Magnitudes.- 6.17 Aktinometrie der Sterne der B.D. bis zur Grösse 7.5 in der Zone 0 ° bis + 20 ° Deklination. Teil A / Actinometry of B.D. Stars down to Magnitude 7.5 in the Zone between Declinations 0 ° and + 20 ° , Part A (with Br. Meyermann, A. Kohlschütter and O. Birck).- 6.18 Aktinometrie der Sterne der B.D. bis zur Grösse 7.5 in der Zone 0 ° bis + 20 ° Deklination. Teil B / Actinometry of B.D. Stars down to Magnitude 7.5 in the Zone between Declinations 0 ° and +20 ° , Part B (with Br. Meyermann, A. Kohlschütter, O. Birck and W. Dziewulski).- 6.19 Buchbesprechung / Book Review: J.A. Parkhurst, Yerkes Actinometry, Zone + 73 ° to + 90 °.- 6.20 Über die Schleierkorrektion bei der Halbgittermethode zur Bestimmung photographischer Sterngrößen / On the Correction for Fogging in the Half-Grating Method of Determining Photographic Stellar Magnitudes.- 6.21 Vorbemerkung zu / Introduction to: W. Dziewulski, Photographische Größen von Sternen in der Nähe des Nordpols / Photographic Magnitudes of Stars Near the North Pole.- 7. Measuring Techniques, Binary Stars, Variable Stars and Spectroscopy.- 7.1 Ueber Messung von Doppelsternen durch Interferenzen / On Measuring Double Stars by Interference Methods.- 7.2 Zur Bestimmung der Theilungsfehler von Maassstäben / On Determining Dividing Errors of Graduated Scales.- 7.3 Beitrag zur Bestimmung von Radialgeschwindigkeiten mit dem Objektivprisma / Contribution on the Determination of Radial Velocities with an Objective Prism.- 7.4 Einige Beobachtungen der Radialgeschwindigkeit von 0: Coronae borealis mit dem Objektivprisma / Some Observations of the Radial Velocity of 0: Coronae borealis with an Objective Prism.- 7.5 über die Radialgeschwindigkeit des Sterns 63 Tauri / On the Radial Velocity of the Star 63 Tauri.- 7.6 Präzisionstechnik und wissenschaftliche Forschung / Precision Engineering and Scientific Research.- 7.7 Spectral Classification of Stars (in German).- 7.8 Ein Verfahren der Bahnbestimmung bei spectroskopischen Doppelsternen / A Procedure for Deterrnining the Orbits of Spectroscopic Binaries.- 7.9 Beobachtungen von Veränderlichen Sternen und der Nova Aurigae / Observations of Variable Stars and of Nova Aurigae.- 7.10 Ein neuer Veränderlicher (41.1910 Tauri) in den Hyaden / A New Variable (41.1910 Tauri) in the Hyades.- 7.11 über den Lichtwechsel des Veränderlichen 41.1910 Tauri / On the Variations in Brightness of the Variable 41.1910 Tauri.- 7.12 Nova 18.1912 Geminorum (Bemerkung zum Spektrum der Eneboschen Nova) /Nova 18.1912 Geminorum (Remark on the Spectrum of Enebo’s Nova).- 7.13 Der neue Stern in den Zwillingen / The New Star in the Constellation Gemini.- for Volume 1.- for Volume 3.

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Book SynopsisIt would seem that any specialist in plasma physics studying a medium in which the interaction between particles is as distance-dependent as the inter­ action between stars and other gravitating masses would assert that the role of collective effects in the dynamics of gravitating systems must be decisive. However, among astronomers this point of view has been recog­ nized only very recently. So, comparatively recently, serious consideration has been devoted to theories of galactic spiral structure in which the dominant role is played by the orbital properties of individual stars rather than collec­ tive effects. In this connection we would like to draw the reader's attention to a difference in the scientific traditions of plasma physicists and astrono­ mers, whereby the former have explained the delay of the onset of controlled thermonuclear fusion by the "intrigues" of collective processes in the plasma, while many a generation of astronomers were calculating star motions, solar and lunar eclipses, and a number of other fine effects for many years ahead by making excellent use of only the laws of Newtonian mechanics. Therefore, for an astronomer, it is perhaps not easy to agree with the fact that the evolution of stellar systems is controlled mainly by collective effects, and the habitual methods of theoretical mechanics III astronomy must make way for the method of self-consistent fields.Table of Contents(Volume I).- § 1. Basic Concepts and Equations of Theory.- § 2. Equilibrium States of Collisionless Gravitating Systems.- § 3. Small Oscillations and Stability.- §4. Jeans Instability of a One—Component Uniform Medium.- §5. Jeans Instability of a Multicomponent Uniform Medium.- 5.1. Basic Theorem (on the Stability of a Multicomponent System with Components at Rest).- 5.2. Four Limiting Cases for a Two—Component Medium.- 5.3. Table of Jeans Instabilities of a Uniform Two—Component Medium.- 5.4. General Case of n Components.- §6. Non—Jeans Instabilities.- § 7. Qualitative Discussion of the Stability of Spherical, Cylindrical (and Disk—Shaped) Systems with Respect to Radial Perturbations.- I Theory.- I Equilibrium and Stability of a Nonrotating Flat Gravitating Layer.- § 1. Equilibrium States of a Collisionless Flat Layer.- § 2. Gravitational (Jeans) Instability of the Layer.- § 3. Anisotropic (Fire—Hose) Instability of a Collisionless Flat Layer.- 3.1. Qualitative Considerations.- 3.2. Derivation of the Dispersion Equation for Bending Perturbations of a Thin Layer.- 3.3. Fire—Hose Instability of a Highly Anisotropic Flat Layer.- 3.4. Analysis of the Dispersion Equation.- 3.5. Additional Remarks.- § 4. Derivation of Integra—Differential Equations for Normal Modes of a Flat Gravitating Layer.- § 5. Symmetrical Perturbations of a Flat Layer with an Isotropic Distribution Function Near the Stability Boundary.- § 6. Perpendicular Oscillations of a Homogeneous Collisionless Layer.- 6.1. Derivation of the Characteristic Equation for Eigenfrequencies.- 6.2. Stability of the Model.- 6.3. Permutational Modes.- 6.4. Time—Independent Perturbations (? = 0).- Problems.- II Equilibrium and Stability of a Collisionless Cylinder.- §1. Equilibrium Cylindrical Configurations.- § 2. Jeans Instability of a Cylinder with Finite Radius.- 2.1. Dispersion Equation for Eigenfrequencies of Axial-Symmetrical Perturbations of a Cylinder with Circular Orbits of Particles.- 2.2. Branches of Axial—Symmetrical Oscillations of a Rotating Cylinder with Maxwellian Distribution of Particles in.- 2.3. Longitudinal Velocities.- 2.4. Oscillative Branches of the Rotating Cylinder with a Jackson Distribution Function (in Longitudinal Velocities).- 2.5. Axial—Symmetrical Perturbations of Cylindrical Models of a More General Type.- § 3. Nonaxial Perturbations of a Collisionless Cylinder.- 3.1. The Long—Wave Fire-Hose Instability.- 3.2. Nonaxial Perturbations of a Cylinder with Circular Particle Orbits 100§ 4. Stability of a Cylinder with Respect to Flute—like Perturbations.- § 5. Local Analysis of the Stability of Cylinders (Flute—like Perturbations).- 5.1. Dispersion Equation for Model (2), § 1.- 5.2. Maxwellian Distribution Function.- § 6. Comparison with Oscillations of an Incompressible Cylinder.- 6.1. Flute—like Perturbations (kz = 0).- § 7. Flute—like Oscillations of a Nonuniform Cylinder with Circular Orbits of Particles.- Problems.- III Equilibrium and Stability of Collisionless Spherically Symmetrical Systems.- § 1. Equilibrium Distribution Functions.- § 2. Stability of Systems with an Isotropic Particle Velocity Distribution.- 2.1. The General Variational Principle for Gravitating Systems with the Isotropic Distribution of Particles in Velocities (f0 = f0(E), f’0 = df0|dE ? 0).- 2.2. Sufficient Condition of Stability.- 2.3. Other Theorems about Stability. Stability with Respect to Nonradial Perturbations.- 2.4. Variational Principle for Radial Perturbations.- 2.5. Hydrodynamical Analogy.- 2.6. On the Stability of Systems with Distribution Functions That Do Not Satisfy the Condition f’0 (E) ? 0.- § 3. Stability of Systems of Gravitating Particles Moving On Circular Trajectories.- 3.1. Stability of a Uniform Sphere.- 3.2. Stability of a Homogeneous System of Particles with Nearly Circular Orbits.- 3.3. Stability of a Homogeneous Sphere with Finite Angular Momentum.- 3.4. Stability of Inhomogeneous Systems.- § 4. Stability of Systems of Gravitating Particles Moving in Elliptical Orbits.- 4.1. Stability of a Sphere with Arbitrary Elliptical Particle Orbits.- 4.2. Instability of a Rotating Freeman Sphere.- § 5. Stability of Systems with Radial Trajectories of Particles.- 5.1. Linear Stability Theory.- 5.2. Simulation of a Nonlinear Stage of Evolution.- § 6. Stability of Spherically Symmetrical Systems of General Form.- 6.1. Series of the Idlis Distribution Functions.- 6.2. First Series of Camm Distribution Functions (Generalized Poly tropes).- 6.3. Shuster’s Model in the Phase Description.- §7. Discussion of the Results.- Problems.- IV Equilibrium and Stability of Collisionless Ellipsoidal Systems.- § 1. Equilibrium Distribution Functions.- 1.1 Freeman’s Ellipsoidal Models.- 1.2. “Hot” Models of Collisionless Ellipsoids of Revolution.- § 2. Stability of a Three—Axial Ellipsoid and an Elliptical Disk.- 2.1. Stability of a Three-Axial Ellipsoid.- 2.2. Stability of Freeman Elliptical Disks.- § 3. Stability of Two—Axial Collisionless Ellipsoidal Systems.- 3.1. Stability of Freeman’s Spheroids.- 3.2. Peebles—Ostriker Stability Criterion. Stability of Uniform Ellipsoids, “Hot” in the Plane of Rotation.- 3.3. The Fire-Hose Instability of Ellipsoidal Stellar Systems.- 3.4. Secular and Dynamical Instability. Characteristic Equation for Eigenfrequencies of Oscillations of Maclaurin Ellipsoids.- Problems.- V Equilibrium and Stability of Flat Gravitating Systems.- § 1. Equilibrium States of Flat Gaseous and Collisionless Systems.- 1.3. Systems with Circular Particle Orbits.- 1.4. Plasma Systems with a Magnetic Field.- 1.5. Gaseous Systems.- 1.6. “Hot” Collisionless Systems.- § 2. Stability of a “Cold” Rotating Disk.- 2.1. Membrane Oscillations of the Disk.- 2.2. Oscillations in the Plane of the Disk.- § 3. Stability of a Plasma Disk with a Magnetic Field.- 3.1. Qualitative Derivation of the Stability Condition.- 3.2. Variational Principle.- 3.3. Short—Wave Approximation.- 3.4. Numerical Analysis of a Specific Model.- § 4. Stability of a “Hot” Rotating Disk.- 4.1. Oscillations in the Plane of the Disk.- 4.2. Bending Perturbations.- 4.3. Methods of the Stability Investigation of General Collisionless Disk Systems.- 4.4. Exact Spectra of Small Perturbations.- 4.5. Global Instabilities of Gaseous Disks. Comparison of Stability Properties of Gaseous and Stellar Disks.- Problems.- References.- Additional References.

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Table of Contents(Volume II).- Non-Jeans Instabilities of Gravitating Systems.- VI Non-Jeans Instabilities of Gravitating Systems.- § 1. Beam Instability of a Gravitating Medium.- 1.1. Theorem of a Number of Instabilities of the Heterogeneous System with Homogeneous Flows.- 1.2. Expression for the Growth Rate of the Kinetic Beam Instability in the Case of a Beam of Small Density (for an Arbitrary Distribution Function).- 1.3. Beam with a Step Function Distribution.- 1.4. Hydrodynamical Beam Instability. Excitation of the Rotational Branch.- 1.5. Stabilizing Effect of the Interaction of Gravitating Cylinders and Disks.- 1.6. Instability of Rotating Inhomogeneous Cylinders with Oppositely Directed Beams of Equal Density.- § 2. Gradient Instabilities of a Gravitating Medium.- 2.1. Cylinder of Constant Density with Radius-Dependent Temperature. Hydrodynamical Instability.- 2.2. Cylinder of Constant Density with a Temperature Jump. Kinetic Instability.- 2.3. Cylinder with Inhomogeneous Density and Temperature.- § 3. Hydrodynamical Instabilities of a Gravitating Medium with a Growth Rate Much Greater than that of Jeans.- 3.1. Hydrodynamical Instabilities in the Model of a Flat Parallel Flow.- 3.2. Hydrodynamical Instabilities of a Gravitating Cylinder.- §4. General Treatment of Kinetic Instabilities.- 4.1. Beam Effects in the Heterogeneous Model of a Galaxy.- 4.2. Influence of a “Black Hole” at the Center of a Spherical System on the Resonance Interactions Between Stars and Waves.- 4.3. Beam Instability in the Models of a Cylinder and a Flat Layer.- VII Problems of Nonlinear Theory.- § 1. Nonlinear Stability Theory of a Rotating, Gravitating Disk.- 1.1. Nonlinear Waves and Solitons in a Hydrodynamical Model of an Infinitely Thin Disk with Plane Pressure.- 1.2. Nonlinear Waves in a Gaseous Disk.- 1.3. Nonlinear Waves and Solitons in a Stellar Disk.- 1.4. Explosive Instability.- 1.5. Remarks on the Decay Processes.- 1.6. Nonlinear Waves in a Viscous Medium.- § 2. Nonlinear Interaction of a Monochromatic Wave with Particles in Gravitating Systems.- 2.1. Nonlinear Dynamics of the Beam Instability in a Cylindrical Model.- 2.2. Nonlinear Saturation of the Instability at the Corotation Radiusin the Disk.- § 3. Nonlinear Theory of Gravitational Instability of a Uniform Expanding Medium.- § 4. Foundations of Turbulence Theory.- 4.1. Hamiltonian Formalism for the Hydrodynamical Model of a Gravitating Medium.- 4.2. Three-Wave Interaction.- 4.3. Four-Wave Interaction.- §5. Concluding Remarks.- 5.1. When Can an Unstable Gravitating Disk be Regarded as an Infinitesimally Thin One?.- 5.2. On Future Soliton Theory of Spiral Structure.- Problems.- II Astrophysical Applications.- VIII General Remarks.- § 1. Oort’s Antievolutionary Hypothesis.- § 2. Is There a Relationship Between the Rotational Momentum of an Elliptical Galaxy and the Degree of Oblateness?.- § 3. General Principles of the Construction of Models of Spherically Symmetric Systems.- § 4. Lynden-Bell’s Collisionless Relaxation.- § 5. Estimates of “Collisionlessness” of Particles in Different Real Systems.- IX Spherical Systems.- § 1. A Brief Description of Observational Data.- 1.1. Globular Star Clusters.- 1.2. Spherical Galaxies.- 1.3. Compact Galactic Clusters.- § 2. Classification of Unstable Modes in Scales.- § 3. Universal Criterion of the Instability.- § 4. Specificity of the Effects of Small-Scale and Large-Scale Perturbations on the System’s Evolution.- § 5. Results of Numerical Experiments for Systems with Parameters Providing Strong Supercriticality.- § 6. Example of Strongly Unstable Model.- § 7. Can Lynden-Bell’s Intermixing Mechanism Be Observed Against a Background of Strong Instability ?.- § 8. Is the “Unstable” Distribution of Stellar Density Really Unstable (in the Hydrodynamical Sense) in the Neighborhood of a “Black Hole”?.- X Ellipsoidal Systems.- § 1. Objects Under Study.- § 2. Elliptical Galaxies.- 2.1. Why Are Elliptical Galaxies More Oblate than E7 Absent?.- 2.2. Comparison of the Observed Oblatenesses of S- and SO-Galaxies with the Oblateness of E-Galaxies.- 2.3. Two Possible Solutions of the Problem.- 2.4. The Boundary of the Anisotropic (Fire-Hose) Instability Determines the Critical Value of Oblateness.- 2.5. Universal Criterion of Instability.- §3. SB-Galaxies.- 3.1. The Main Problem.- 3.2. Detection in NGC 4027 of Counterflows as Predicted by Freeman.- 3.3. Stability of Freeman Models of SB-Galaxies with Observed Oblateness.- XI Disk-like Systems. Spiral Structure.- § 1. Different Points of View on the Nature of Spiral Structure.- § 2. Resonant Interaction of the Spiral Wave with Stars of the Galaxy.- 2.1. Derivation of Expressions for the Angular Momentum and Energy of the Spiral Wave.- 2.2. Physical Mechanisms of Energy and Angular Momentum Exchange Between the Spiral Waves and the Resonant Stars.- § 3. The Linear Theory of Stationary Density Waves.- 3.1. The Primary Idea of Lin and Shu of the Stationary Density Waves.- 3.2. The Spiral Galaxy as an Infinite System of Harmonic Oscillators.- 3.3. On “Two-Armness” of the Spiral Structure.- 3.4. The Main Difficulties of the Stationary Wave Theory of Lin and Shu.- §4. Linear Theory of Growing Density Waves.- 4.1. Spiral Structure as the Most Unstable Mode.- 4.2. Gravitational Instability at the Periphery of Galaxies.- 4.3. Waves of Negative Energy Generated Near the Corotation Circle and Absorbed at the Inner Lindblad Resonance—Lynden-BellKalnaj’s Picture of Spiral Pattern Maintenance.- 4.4. Kelvin–Helmholz Instability and Flute-like Instability in the Near-Nucleus Region of the Galaxy as Possible Generators of Spiral Structure.- 4.5. The “Trailing” Character of Spiral Arms.- § 5. Comparison of the Lin–Shu Theory with Observations.- 5. 1 The Galaxy.- 5.2. M33, M51, M81.- § 6. Experimental Simulation of Spiral Structure Generation.- 6. 1 In a Rotating Laboratory Plasma.- 6.2. In Numerical Experiment.- § 7. The Hypothesis of the Origin of Spirals in the SB-Galaxies.- XII Other Applications.- § 1 On the Structure of Saturn’s Rings.- l.1. Introduction.- 1.2. Model. Basic Equations.- 1.3. Jeans Instability.- 1.4. Dissipative Instabilities.- 1.5. Modulational Instability.- Appendix. Derivation of the Expression for the Perturbation Energy of Maclaurin’s Ellipsoid.- § 2. On the Law of Planetary Distances.- §3. Galactic Plane Bending.- 3.1. Quasistationary Tidal Deformation.- 3.2. Free Modes of Oscillations.- 3.3. Close Passage.- § 4. Instabilities in Collisions of Elementary Particles.- § 1. Collisionless Kinetic Equation and Poisson Equation in Different Coordinate Systems.- § 2. Separation of Angular Variables in the Problem of Small Perturbations of Spherically Symmetrical Collisionless Systems.- § 3. Statistical Simulation of Stellar Systems.- 3.1. Simulation of Stellar Spheres of the First Camm Series.- 3.2. Simulation of Homogeneous Nonrotating Ellipsoids.- § 4. The Matrix Formulation of the Problem of Eigenoscillations of a Spherically-Symmetrical Collisionless System.- § 5. The Matrix Formulation of the Problem of Eigenoscillations of Collisionless Disk Systems.- 5.1. The Main Ideas of the Derivation of the Matrix Equation.- 5.2. “Lagrange” Derivation of the Matrix Equation.- § 6. Derivation of the Dispersion Equation for Perturbations of the Three-Axial Freeman Ellipsoid.- § 7. WKB Solutions of the Poisson Equation Taking into Account the Preexponential Terms and Solution of the Kinetic Equation in the Postepicyclic Approximation.- 7.1. The Relation Between the Potential and the Surface Density.- 7.2. Calculations of the Response of a Stellar Disk to an Imposed Perturbation of the Potential.- § 8. On the Derivation of the Nonlinear Dispersion Equation for Collisionless Disk.- § 9. Calculation of the Matrix Elements for the Three-Waves Interaction.- § 10. Derivation of the Formulas for the Boundaries of Wave Numbers Range Which May Take Part in a Decay.- §11. Derivation of the Kinetic Equation for Waves.- § 12. Table of Non-Jeans Instabilities (with a Short Summary).- References.- Additional References.

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Book SynopsisDie Spezielle Relativitätstheorie steht und fällt mit der universellen Konstanz der Lichtgeschwindigkeit. Darauf gründet die Einstein-Minkowski-Axiomatik, die wegen ihrer grundsätzlichen Bedeutung in keinem Lehrbuch zur Theoretischen Physik fehlen darf. Hier soll außerdem auf eine zweite, unabhängige, aber vollkommen äquivalente axiomatische Darstellung aufmerksam gemacht werden, die weniger abstrakt und daher geeignet ist, auch demjenigen einen Einstieg in die relativistische Welt zu erschließen, der nicht unbedingt theo­re­tischer Physiker werden will. Dabei geht es dann primär um den Gang von bewegten und ruhenden Uhren und die Längen von bewegten und ruhenden Maßstäben. Ganz wesentlich ist es, von Anfang an den definitorischen Charakter bei der Bestimmung des Begriffes der Gleichzeitigkeit zu verstehen. Der sorgfältige Umgang mit dieser Definition liefert den Schlüssel zur Auflösung der relativistischen Paradoxa, wie dies ausführlich beim Zwillingsparadoxon gezeigt wird. Die Unterscheidung von Korrelation und Wechselwirkung erlaubt eine Betrachtung von Tachyonen, ohne die Kausalität zu verletzen. Anhand eines Gittermodells der relativistischen Raum-Zeit kann am Ende sogar das Zustandekommen der Längenkontraktion, der Zeitdilatation und der relativistischen Massenformel veranschaulicht werden. Es werden die Schlüsselexperimente erklärt und 48 Übungsaufgaben vorgerechnet.Table of Contents​Das Relativitätsprinzip: klassische und relativistische Raum-Zeit.- Energie - Masse - Äquivalenz.- Relativistische Phänomene und Paradoxa.- Die Darstellungen der Lorentz-Gruppe.- Mechanik, Elektrodynamik, Weyl-Gleichung, Dirac-Gleichung, Pauli-Gleichung.- Ein Gittermodell der relativistischen Raum-Zeit.

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Book SynopsisThis book discusses the state of the art of the basic theoretical and observational topics related to black hole astrophysics. It covers all the main topics in this wide field, from the theory of accretion disks and formation mechanisms of jet and outflows, to their observed electromagnetic spectrum, and attempts to measure the spin of these objects. Black holes are one of the most fascinating predictions of general relativity and are currently a very hot topic in both physics and astrophysics. In the last five years there have been significant advances in our understanding of these systems, and in the next five years it should become possible to use them to test fundamental physics, in particular to predict the general relativity in the strong field regime. The book is both a reference work for researchers and a textbook for graduate students. Trade Review“A perfect volume for young scientists starting their research in a field of astrophysics of black holes. The book presents very deep and broad knowledge on the topic, in a well-written form, which can easily be understood by the reader. It is also very good position for more advanced scientists as well.” (Hubert Siejkowski, Pure and Applied Geophysics, Vol 175, 2018)Table of ContentsPreface.- Black Hole Accretion Discs.- Black hole X-ray binaries.- Measuring spin: implications for our understanding of black hole accretion physics.- Jet and wind from black hole accretion flows.- Gravitational Waves: a new tool for observing the Universe.- A brief review of relativistic gravitational collapse.- General relativity in a nutshell.

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