Gravity Books

Book SynopsisGalilei manifolds.- Classical Newton–Cartan gravity.- Galilei manifolds via principal bundles.- Semidirect extensions of principal bundles.- Bargmann structures.- Outlook.- Appendix A Semidirect products of Lie groups.

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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 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 SynopsisOur esteemed colleague C. V. Vishveshwara, popularly known as Vishu, turned sixty on 6th March 1998. His colleagues and well wishers felt that it would be appropriate to celebrate the occasion by bringing out a volume in his honour. Those of us who have had the good fortune to know Vishu, know that he is unique, in a class by himself. Having been given the privilege to be the volume's editors, we felt that we should attempt something different in this endeavour. Vishu is one of the well known relativists from India whose pioneer­ ing contributions to the studies of black holes is universally recognised. He was a student of Charles Misner. His Ph. D. thesis on the stability of the Schwarzschild black hole, coordinate invariant characterisation of the sta­ tionary limit and event horizon for Kerr black holes and subsequent seminal work on quasi-normal modes of black holes have passed on to become the starting points for detailed mathematical investigations on the nature of black holes. He later worked on other aspects related to black holes and compact objects. Many of these topics have matured over the last thirty years. New facets have also developed and become current areas of vigorous research interest. No longer are black holes, ultracompact objects or event horizons mere idealisations of mathematical physicists but concrete entities that astrophysicists detect, measure and look for. Astrophysical evidence is mounting up steadily for black holes.Table of ContentsPreface. 1. The Black Hole Equilibrium Problem; B. Carter.2. Stability of Black Holes; B.F. Whiting. 3. Separability of Wave Equations; E.G. Kalnins, et al. 4. Energy-Conservation Laws for Perturbed Stars and Black Holes; V.Ferrari. 5. Gravitational Collapse and Cosmic Censorship; R.M.Wald. 6. Disturbing the Black Hole; J.D. Bekenstein.7. Notes on Black Hole Fluctuations and Back-Reaction; B.L. Hu, et al. 8. Black Holes in Higher Curvature Gravity; R.C. Myers. 9. Micro-Structure of Black Holes and String Theory; S. Wadia. 10. Quantum Geometry and Black Holes; A. Ashtekar, K. Krasnov. 11. Black Holes, Global Monopole Charge and Quasi-Local Energy; N. Dadhich. 12. Kinematical Consequences of Inertial Forces in General Relativity; A.R. Prasanna, S. Iyer. 13. Gyroscopic Precession and Inertial Forces in General Relativity; R.Nayak. 14. Analysis of the Equilibrium of a Charged Test Particlein the Kerr - Newman Black Hole; J.M. Aguirregabiria, et al. 15. Neutron Stars and Relativistic Gravity; M. Vivekanand. 16. Accretion Disks around Black Holes; P.J. Wiita. 17. Astrophysical Evidence for Black Hole Event Horizons; K. Menou, et al. 18. Black Holes in Active Galactic Nuclei; A.K. Kembhavi. 19. Energetic Photon Spectra as Probes of the Process of Particle Acceleration in Accretion Flows around Black Holes; R. Cowsik. 20. Black Hole Perturbation Approach to Gravitational Radiation: Post-Newtonian Expansion for Inspiralling Binaries; M.Sasaki. 21. More Quasi Than Normal! N. Andersson. 22. The Two Black Hole Problem: Beyond Linear Perturbations; R.H. Price. 23. The Synergy between Numerical and Perturbative Approaches to Black Holes; E. Seidel. 24. Cauchy-Characteristic Matching; N.T. Bishop, et al. 25. Astrophysical Sources of Gravitational Waves; B.S. Sathyaprakash.26. Gravitational Radiation from Inspiraling Compact Binaries: Motion, Generation and Radiation Reaction; B.R. Iyer. 27. Ground-Based Interferometric Detectors of Gravitational Waves; B. Bhawal. 28. Detection of Gravitational Waves from Inspiraling Compact Binaries; S.V. Dhurandhar. 29. Perturbations of Cosmological Backgrounds; P.K.S. Dunsby, G.F.R. Ellis. 30.Mach's Principle in Electrodynamics and Inertia; J.V. Narlikar.31. The Early History of Quantum Gravity (1916&endash;1940); J. Stachel. 32. Geometry in Color Perception; A. Ashtekar, etal. 33. C.V. Vishveshwara &endash; A Profile; N. Panchapakesan. Publications of C.V. Vishveshwara.

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Book SynopsisRon Cowen offers a sweeping account of the century of experimentation that has consistently confirmed Einstein's general theory of relativity. He shows how we got from Eddington's pivotal observations of the 1919 eclipse to the Event Horizon Telescope, aimed at starlight wrapping around the black hole at our galaxy's center.Trade ReviewCowen is a gifted science writer and storyteller, and the story is amazing! -- John C. Mather, winner of the Nobel Prize in Physics[Cowen’s] brisk, engaging narrative leads us from Einstein’s famous ‘thought experiments’ through theorists’ many (so far unsuccessful) attempts to marry quantum mechanics with general relativity, and up to recent (more successful) efforts to observe gravitational waves and black holes. * Wall Street Journal *There are some extremely clever ways to visualize how gravitation works in a Universe governed by General Relativity under a wide variety of physical conditions, and Cowen explores many of the classic ways you've probably seen before along with some incredibly creative ones that were new, even to me. -- Ethan Siegel * Forbes *A brief, accessible account of the 1919 eclipse and subsequent advances in cosmology, touching upon dark matter, dark energy, quantum gravity, and black holes. It’s a very quick and readable introduction to some of the exotic findings that came in Einstein’s wake. * Bookforum *This is as good a short introduction to Einstein’s thought as one could wish for. -- Simon Ings * The Spectator *In a conversational style, the veteran physics writer chronicles the field’s greatest hits in the century since a solar eclipse proved Einstein was right. -- Gemma Tarlach * Discover *A breezy and enjoyable read, a welcome addition to a crowded shelf of books on these topics. -- Peter Coles * Nature *Gravity’s Century is remarkably easy to follow and read. If you are a keen beginner, or just interested in some of the people behind the science, read this book. -- Laura Nuttall * BBC Sky at Night *This gracefully written history of 20th-century gravity research from science writer Cowen shines a light on a key aspect of modern physics…Filled with vivid descriptions of cutting-edge work and the scientists behind it, Cowen’s book is fascinating, both a learning experience and a pleasure to read. * Publishers Weekly (starred review) *A clear and compelling narrative about the development of our understanding of gravity and the universe, powered by Einstein and his cohorts. Cowen weaves together the historical and personal events leading to this revolution and brings us up to date with the ideas and speculations that will likely forge an even newer and more radical understanding of the nature of the world. -- George F. Smoot, winner of the Nobel Prize in PhysicsEinstein’s general theory of relativity radically changed our notions of space, gravity, and time. Gravity’s Century takes us from Einstein’s struggle to develop his theory up to the modern day—when the detection of gravitational waves from black holes has confirmed general relativity’s most audacious claims, even as scientists are still trying to reconcile the theory with the other great idea of twentieth-century physics, quantum mechanics. -- David Spergel, Princeton UniversityAccessible and compact…A great introduction to Einstein’s theory of general relativity and the century of research that has been testing his ideas since. -- Leon Vlieger * Inquisitive Biologist *A concise chronicle of the dramatic expansion of our knowledge of the universe, from the eclipse expeditions of 1919 to test Einstein’s theory of relativity, to the Event Horizon Telescope’s black hole images of 2019. -- Mike Perricone * Symmetry *Clear and readily intelligible to the non-specialist. -- Johannes E. Riutta * Well-Read Naturalist *Its informal, readable style hides an enormous amount of physics and a fair share of history. * Choice *[An] enjoyable read…Cowen does a good job of breaking down ideas so that they are easily understood…I would recommend Gravity’s Century to anyone with an interest in astrophysics in general, or in gravitation in particular. -- Earl Patrick Bellinger * Metascience *

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Book Synopsis9% nothing, but the thoughts it will inspire are massive.Trade Review[James'] conversational and at times humourous approach attempts to re-inspire the audience to look more closely at everything around them... If you'd like to understand more about how science affects the world around you without complicated scientific jargon that goes with it, this book is for you. It's an informative and accessible read that'll make you rethink whether taking the rubbish out is as boring as you previously thought. -- Nina Pace Cosmos 2011 James provides a satisfying and entertaining read for those of us who have a latent curiosity, for those who watch Nova or listen to Stephen Hawking and are still left scratching our heads, for those with curious children who demand more than "just because" in answer to their questions, and for science teachers looking for student-friendly explanations... she doesn't claim to have the mathematical intelligence of Einstein, but she has something he didn't: the ability to explain esoteric scientific theories and concepts so that you understand them. -- Ruth Douillette Internet Review of Books 2011Table of ContentsPrefaceAcknowledgmentsIntroduction1. Nights1.1. Of Snowballs and Ice-Skaters1.2. Putting the Brakes On1.3. Why Is Space Dark? Answer #1: Location, Location, Location1.4. Why Is Space Dark? Answer #2: Because1.5. Why Is Space Dark? Answer #3: Actually It Isn'tSmall Wonder: Day and Night on MercurySmall Wonder: Keeping the Night Sky Dark2. Light2.1. Codebreaking Basics2.2. The Little Orphan Annie Secret Decoder CD2.3. More Than Meets the Eye2.4. Evading the Question2.5. Making Light of the UniverseSmall Wonder: Why Is the Sky Blue? And Why Are Sunsets Red?Small Wonder: The Early Universe—A Made-for-TV Movie!3. Stuff3.1. It's Element-ary3.2. Element Factories3.3. In the Beginning . . .3.4. Making Light of Evil Twins3.5. The Good Guys Always Win . . . But Why?Small Wonder: What Are You Really Made Of?4. Gravity4.1. A Penny for Your Thoughts?4.2. Earth, the 6 Trillion Trillion Kilogram Weakling4.3. Of Apples and Orbits and Confused Astronauts4.4. But Wait . . . There's More!4.5. Surprise! Gravity Isn't a Force!Small Wonder: How to Lose Weight and Keep It Off, Guaranteed!5. Time5.1. Got a Second?5.2. Time in a Bottle—or in a Black Hole5.3. A One-Way Ticket to Disorder5.4. Time: The Grand Illusion?Small Wonder: So What Causes Daylight Saving Time to Happen?Small Wonder: Why Are There Seven Days in a Week?Small Wonder: What Would Happen if You Fell into a Black Hole?6. Home6.1. Goldilocks and the Three Planets6.2. Goldilocks and the Three Stars6.3. Goldilocks in Suburbia, Traffic, and Time6.4. Why Goldilocks Could Never Have Been a Successful Real Estate AgentSmall Wonder: Looking for a Home Away from HomeSmall Wonder: Do Aliens Exist?Small Wonder: No, Really. Do Aliens Exist?Small Wonder: Wanted—Alien Hunters7. Wonder7.1. Life—The Ultimate Eating Machine7.2. There's More to Life Than Eating7.3. It's All in Your Head . . . Maybe7.4. It's a Wonder-Full LifeSmall Wonder: Small WondersAfterwordFor Further ReadingIndex

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Book Synopsis9% nothing, but the thoughts it will inspire are massive.Trade Review[James'] conversational and at times humourous approach attempts to re-inspire the audience to look more closely at everything around them... If you'd like to understand more about how science affects the world around you without complicated scientific jargon that goes with it, this book is for you. It's an informative and accessible read that'll make you rethink whether taking the rubbish out is as boring as you previously thought. -- Nina Pace Cosmos 2011 James provides a satisfying and entertaining read for those of us who have a latent curiosity, for those who watch Nova or listen to Stephen Hawking and are still left scratching our heads, for those with curious children who demand more than "just because" in answer to their questions, and for science teachers looking for student-friendly explanations... she doesn't claim to have the mathematical intelligence of Einstein, but she has something he didn't: the ability to explain esoteric scientific theories and concepts so that you understand them. -- Ruth Douillette Internet Review of Books 2011Table of ContentsPrefaceAcknowledgmentsIntroduction1. Nights1.1. Of Snowballs and Ice-Skaters1.2. Putting the Brakes On1.3. Why Is Space Dark? Answer #1: Location, Location, Location1.4. Why Is Space Dark? Answer #2: Because1.5. Why Is Space Dark? Answer #3: Actually It Isn'tSmall Wonder: Day and Night on MercurySmall Wonder: Keeping the Night Sky Dark2. Light2.1. Codebreaking Basics2.2. The Little Orphan Annie Secret Decoder CD2.3. More Than Meets the Eye2.4. Evading the Question2.5. Making Light of the UniverseSmall Wonder: Why Is the Sky Blue? And Why Are Sunsets Red?Small Wonder: The Early Universe—A Made-for-TV Movie!3. Stuff3.1. It's Element-ary3.2. Element Factories3.3. In the Beginning . . .3.4. Making Light of Evil Twins3.5. The Good Guys Always Win . . . But Why?Small Wonder: What Are You Really Made Of?4. Gravity4.1. A Penny for Your Thoughts?4.2. Earth, the 6 Trillion Trillion Kilogram Weakling4.3. Of Apples and Orbits and Confused Astronauts4.4. But Wait . . . There's More!4.5. Surprise! Gravity Isn't a Force!Small Wonder: How to Lose Weight and Keep It Off, Guaranteed!5. Time5.1. Got a Second?5.2. Time in a Bottle—or in a Black Hole5.3. A One-Way Ticket to Disorder5.4. Time: The Grand Illusion?Small Wonder: So What Causes Daylight Saving Time to Happen?Small Wonder: Why Are There Seven Days in a Week?Small Wonder: What Would Happen if You Fell into a Black Hole?6. Home6.1. Goldilocks and the Three Planets6.2. Goldilocks and the Three Stars6.3. Goldilocks in Suburbia, Traffic, and Time6.4. Why Goldilocks Could Never Have Been a Successful Real Estate AgentSmall Wonder: Looking for a Home Away from HomeSmall Wonder: Do Aliens Exist?Small Wonder: No, Really. Do Aliens Exist?Small Wonder: Wanted—Alien Hunters7. Wonder7.1. Life—The Ultimate Eating Machine7.2. There's More to Life Than Eating7.3. It's All in Your Head . . . Maybe7.4. It's a Wonder-Full LifeSmall Wonder: Small WondersAfterwordFor Further ReadingIndex

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Book Synopsis1 Relativity Before 1905.- 2 Special Relativity-Kinematics.- 3 Special Relativity-Kinetics.- 4 Arbitrary Frames.- 5 Surfaces and Curvature.- 6 Intrinsic Geometry.- 7 General Relativity.- 8 Consequences.Table of Contents1 Relativity Before 1905.- 2 Special Relativity-Kinematics.- 3 Special Relativity-Kinetics.- 4 Arbitrary Frames.- 5 Surfaces and Curvature.- 6 Intrinsic Geometry.- 7 General Relativity.- 8 Consequences.

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Book SynopsisThis textbook gradually introduces the reader to several topics related to black hole physics with a didactic approach. It starts with the most basic black hole solution, the Schwarzschild metric, and discusses the basic classical properties of black hole solutions as seen by different probes. Then it reviews various theorems about black hole properties as solutions to Einstein gravity coupled to matter fields, conserved charges associated with black holes, and laws of black hole thermodynamics. Next, it elucidates semiclassical and quantum aspects of black holes, which are relevant in ongoing and future research. The book is enriched with many exercises and solutions to assist in the learning.The textbook is designed for physics graduate students who want to start their research career in the field of black holes; postdocs who recently changed their research focus towards black holes and want to get up-to-date on recent and current research topics; advanced researchers intending to teach (or learn) basic and advanced aspects of black hole physics and the associated mathematical tools. Besides general relativity, the reader needs to be familiar with standard undergraduate physics, like thermodynamics, quantum mechanics, and statistical mechanics. Moreover, familiarity with basic quantum field theory in Minkowski space is assumed. The book covers the rest of the needed background material in the main text or the appendices.Table of ContentsChapter I: INTRODUCTION1. A brief review on essentials of General Relativity, from basic concepts, mathematical frameworkand Einstein equations Einstein-Hilbert action and classical tests of GR;2. Brief review of history and timeline of developments from Schwarzschild solution to black holemergers and to information paradox and rewall;3. Gravitational collapse and Chandrasekhar mass bound;4. Different schools of thought on black holes: high energy oriented, GR oriented and quantuminformation theory oriented; open issue how to merge these schoolsChapter II: BASIC CONCEPTS and TOOLS1. Schwarzschild metric and some basic facts and analysis;2. Analysis of geodesics, notion of Killing horizon and near horizon Rindler geometry;3. Kruskal coordinates, maximal extensions and Carter-Penrose diagram;4. Einstein-Maxwell theory and Reisner-Nordström solution and its basic analysis;5. Kerr solution and its basic analysis;6. Black holes in (A)dS backgrounds.Chapter III: CLASSICAL ASPECTS1. Lensing and black hole shadows;2. Super-radiance, Penrose process and black hole mining;3. Gravitational wave emission in black hole mergers;4. Accretion disk physics;5. Extremal black holes, their near horizon and basic analysis.Chapter IV: ADVANCED CONCEPTS1. Mathematical defnition of black holes, notion of various different horizons, Killing, event,cosmological, isolated; trapped surface.2. Conjectures and theorems (Cosmic censorship; Penrose mass inequality, singularity, uniquenessand topology theorems)3. Raychaudhuri equation and area theorem (2nd law); energy conditions;4. Linear and nonlinear stability of black hole solutions;5. More detailed analysis of collapse, Choptuik exponents and critical exponents;6. Canonical boundary charges (1st law), ADM, Brown-York, Regge-Teitelboim, Iyer-Wald-Zoupas,Barnich-Brandt and Hajian-Sh-J charges.7. Variation principle; Gibbons-Hawking-York boundary term; Brown-York stress tensor;8. Quasi-normal modes and black hole perturbations;9. Four laws of black hole thermodynamics and their new derivations a la Wald-Hajian-Sh-J;Chapter V: SEMICLASSICAL ASPECTS1. Quantization on black hole backgrounds;2. Unruh effect;3. Hawking effect;4. Bekenstein entropy and the area law, the Bekenstein bound;5. Parikh-Wilczek tunneling;6. Black hole evaporation;7. Membrane paradigm.Chapter VI: EXPERT TOPICS1. Gravity in lower dimensions (including various asymptotic symmetry algebras)2. Gravity in higher dimensions (including a brief discussion on supergravity);3. Higher dimensional black hole/ring/brane solutions.4. Aspects of holography - holographic renormalization, correlation functions and asymptoticsymmetries5. Extremal black holes and attractor mechanism6. Kerr/CFT and related topics7. Soft hair and black hole microstates.Chapter VII: QUANTUM ASPECTS1. Black holes in string theory;2. Microstate counting;3. Microstate identification/constructions, fuzzballs, fluffballs;4. Information paradox and black hole complementarity and firewalls;5. Black holes and quantum gravity;6. Information paradox and the AdS/CFT;7. Holography, Quantum information (entanglement entropy, Bousso bound, QNEC etc.) andgeneralized laws of black hole thermodynamics.Chapter VIII: OUTLOOK1. Summary;2. Outlook and open issues; - Experimental/observational prospects - Black holes as a window to Quantum Gravity - gravity may be emergent | what does it emerge from?Chapter IX: SOLUTIONS TO EXERCISESWe present numerous exercises throughout the book and in this chapter we give solutions to aselected subset of them.AppendicesWe intend to have some appendices in which we present some details of crucial mathematicalframeworks and formulations not fitting into the main text, in particular - Cartan formulation - Basics of QFT in curved spacetime - Covariant phase space method

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Book SynopsisGraduate students typically enter into courses on string theory having little to no familiarity with the mathematical background so crucial to the discipline. As such, this book, based on lecture notes, edited and expanded, from the graduate course taught by the author at SISSA and BIMSA, places particular emphasis on said mathematical background. The target audience for the book includes students of both theoretical physics and mathematics. This explains the book’s "strange" style: on the one hand, it is highly didactic and explicit, with a host of examples for the physicists, but, in addition, there are also almost 100 separate technical boxes, appendices, and starred sections, in which matters discussed in the main text are put into a broader mathematical perspective, while deeper and more rigorous points of view (particularly those from the modern era) are presented. The boxes also serve to further shore up the reader’s understanding of the underlying math. In writing this book, the author’s goal was not to achieve any sort of definitive conciseness, opting instead for clarity and "completeness". To this end, several arguments are presented more than once from different viewpoints and in varying contexts. Table of ContentsChapter 1. The Polyakov path integral. Chapter 2. Introduction to 2d conformal field theories. Chapter 3. Spectrum, vertices, and BRST quantization. Chapter 4. Tree and one-loop amplitudes in the bosonic string. Chapter 5. Consistent 10d superstring, modular invariance, and all that. Chapter 6. The Heterotic string: part I. Chapter 7. Toroidal compactifications and T-duality (bosonic string). Chapter 8. The Heterotic string: part II. Chapter 9. Superstring interactions and anomalies. Chapter 10. Superstring D-branes. Chapter 11. Strings at strong coupling. Chapter 12. Calabi-Yau compactifications. Appendix.

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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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