Description
Book SynopsisFor about half a century the general theory of relativity attracted little attention from physicists.
Table of ContentsI. The General Theory of Relativity.- 1. Introduction.- 1.1. The Case for Nonflat Space—Time.- 1.2. The Principle of Equivalence.- 1.3. Conflict Between the Equivalence Principle and the Pseudo-Euclidean Metric: Gravitational Redshift.- 1.4. A Fifth Force.- 2. Tensor Calculus and Riemannian Geometry.- 2.1. Riemannian Geometry and the Metric Tensor.- 2.2. Vectors and Tensors.- 2.3. Invariant Volume and Volume Integral.- 2.4. Affine Connection—Parallel Transport.- 2.5. Covariant Differentiation.- 2.6. The Differential Equation of a Geodesic.- 2.7. The Integrability of Parallel Displacement.- 2.8. The Riemann—Christoffel Tensor.- 2.9. The Bianchi Identity.- 2.10. The Ricci Tensor and the Einstein Tensor.- 2.11. The Weyl Tensor.- 2.12. Geodesic Deviation.- 3. Einstein’s Field Equations.- 3.1. Einstein’s Formulation of the Field Equations.- 3.2. Weak Field Approximation (Static Case).- 3.3. Gravitational Waves in Weak Field Approximation.- 3.4. Detection of Gravitational Waves.- 3.5. Integration of the Linearized Equations for a Stationary Axially Symmetric Distribution.- 3.6. The Action Principle and the Energy—Momentum Tensors.- 3.7. The Energy—Stress Tensor.- 3.8. The Einstein Equations from the Variational Principle.- 4. The Schwarzschild Metric and Crucial Tests.- 4.1. The Schwarzschild Solution.- 4.2. Birkhoff’s Theorem.- 4.3. Three Crucial Tests.- 4.4. The PPN Formalism.- 4.5. The Schwarzschild or the Spherically Symmetric Black Hole.- 4.6. Frequency Shift of Spectral Lines of Light Emitted by a Collapsing/Exploding Spherical Body.- 4.7. Fall in Apparent Luminosity of a Collapsing Body.- 4.8. Kruskal—Szekeres Coordinates.- 4.9. Historical Note on the Schwarzschild Black Hole.- 5. Electromagnetism in General Relativity.- 5.1. Introduction.- 5.2. The Field of a Charged Particle.- 5.3. Static Electrovac.- 5.4. The Already Unified Field Theory.- 6. Axially Symmetric Fields.- 6.1. The Lie Derivative and the Killing Equation.- 6.2. Static and Stationary Metrics.- 6.3. The Axially Symmetric Static Metric.- 6.4. Weyl’s Canonical Form.- 6.5. The Case of Two Mass Particles.- 6.6. The Schwarzschild Metric in the Form (6.21).- 6.7. Stationary Axisymmetric Vacuum Solutions.- 7. The Kerr Metric or the Rotating Black Hole.- 7.1. The Kerr Metric in Boyer—Lindquist Coordinates.- 7.2. The Black Hole Property.- 7.3. Locally Nonrotating Observers.- 7.4. The Horizon as a Null Surface.- 7.5. The Kerr—Newmann Metric.- 7.6. The Penrose Process.- 8. The Energy—Momentum Pseudotensor of the Gravitational Field and Loss of Energy by Gravitational Radiation.- 8.1. The Pseudo-Energy—Momentum Tensor.- 8.2. Historical Note.- 8.3. Loss of Energy by Gravitational Radiation.- 8.4. The Case of a Binary Star.- 9. Analysis of the Observational Data of the Hulse—Taylor Pulsar. Confirmation of the Einstein Quadrupole Radiation Formula.- II. Relativistic Astrophysics.- 10. White Dwarf Stars.- 10.1. Introduction.- 10.2. The Contraction of a Radiating Star in the Absence of Energy Generation.- 10.3. Degeneracy and the Equation of State.- 10.4. Limiting Mass for White Dwarfs.- 10.5. A Simple Argument for the Mass Limit.- 10.6. Critique of Chandrasekhar’s Result and Later Works.- 10.7. Historical Note.- 10.8. Observational Data on White Dwarfs.- 10.9. The Cooling and Age of White Dwarfs.- 11. Stellar Evolution, Supernovae, and Compact Objects.- 11.1. Introduction.- 11.2. The Evolution of Stars.- 11.3. The Dynamical Collapse.- 11.4. Some Numerical Results.- 11.5. Explosive Processes.- 11.6. Supernova 1987 A.- 12. Pulsars.- 12.1. Introduction.- 12.2. Distance from Dispersion Measure.- 12.3. Identification of Pulsars as Neutron Stars.- 12.4. The Energetics of Pulsar Emission.- 12.5. The Magnetic Field at the Pulsar Surface.- 12.6. The Age of Pulsars.- 12.7. Calculation of the Braking Index.- 12.8. The Nonvacuum Model.- 12.9. Observational Determination of Pulsar Masses.- 12.10. Cooling of Neutron Stars—Theory and Observation.- 12.11. The Influence of Superfluidity.- 12.12. The Influence of Pion Condensation.- 12.13. The Influence of Quarks.- 13. Spherically Symmetric Star Models.- 13.1. Introduction.- 13.2. The Tolman, Oppenheimer—Volkoff Equation.- 13.3. The Equation of State for Cold Catalyzed Matter.- 13.4. A Model of a Neutron Star and the Mass Limits.- 13.5. The Problems of the Upper Mass Limit of Neutron Stars.- 13.6. The Influence of Rotation, etc., on the Mass Limit.- 13.7. Note on the Stability of Compact Objects.- 14. Black Holes.- 14.1. Introduction.- 14.2. The No-Hair Theorem.- 14.3. The Laws of Black Hole Physics.- 14.4. Black Hole Thermodynamics.- 14.5. The Identification of a Black Hole—Cygnus X-1.- 14.6. The Possible Locale of the Occurrence of Black Holes.- 14.7. The Quasi-Steller Objects (Quasars).- 14.8. Gravitational Lens.- 15. Accretion onto Compact Objects.- 15.1. Introduction—Spherically Symmetric Accretion.- 15.2. Disk Accretion.- 15.3. Compact X-Ray Sources.- III. Cosmology.- 16. The Standard Cosmological Model.- 16.1. Introduction to the Friedmann Metric.- 16.2. Elementary Discussion of Standard Cosmology.- 16.3. The Observational Background of Cosmology.- 16.4. Summary.- 17. The Singularity Problem.- 17.1. Introduction.- 17.2. The Raychaudhuri Equation.- 17.3. The Meaning of Shear, Vorticity, and Expansion.- 17.4. An Elementary Singularity Theorem.- 17.5. The Gödel Universe.- 17.6. General Singularity Theorems.- 18. Thermal History of the Universe—Cosmological Nucleosynthesis.- 18.1. The Thermal History.- 18.2. Cosmological Nucleosynthesis.- 19. Structure Formation in the Universe.- 19.1. The Problem.- 19.2. The Linear Growth Formula.- 19.3. Finite Perturbation.- 19:4. Structure Formation with Dark Matter.- 20. Grand Unified Theory and Spontaneous Symmetry Breaking.- 20.1. Introduction.- 20.2. Gauge Fields.- 20.3. Weak Interaction.- 20.4. Strong Interaction and Grand Unification.- 20.5. Baryon Asymmetry and the Baryon/Photon Ratio.- 21. The Inflationary Scenario.- 21.1. Introduction.- 21.2. The Problems in Terms of Entropy.- 21.3. The Vacuum Energy—Stress Tensor and the de Sitter Phase.- 21.4. The Different Models of Inflation.- 21.5. A Critique of the Inflationary Models.- 21.6. Fluctuations in the Inflationary Models.- 22. Concluding Remarks.- Appendix. Differential Forms.- A.1. Introductory Ideas and Definitions.- A.2. Connection 1-Forms and Ricci Rotation Coefficients.- A.3. Cartan’s Equations of Structure.- A.4. Bianchi Identities and Symmetry Properties of the Riemann—Christoffel Tensor.- A.5. An Example of the Calculation of the Riemann—Christoffel Tensor.- References.
