General Relativity, Relativistic Astrophysics and Cosmology

by Raychaudhuri, A. K.; Banerji, S.; Banerjee, A.

• ISBN13: 9780387978130
• ISBN10: 0387978135
• Format: Hardcover
• Copyright: 1992-08-01
• Publisher: Springer Verlag

Table of Contents

Preface
The General Theory of Relativity	p. 1
Introduction	p. 3
The Case for Nonflat Space-Time	p. 3
The Principle of Equivalence	p. 4
Conflict Between the Equivalence Principle and the Pseudo-Euclidean Metric: Gravitational Redshift	p. 6
A Fifth Force	p. 8
Tensor Calculus and Riemannian Geometry	p. 9
Riemannian Geometry and the Metric Tensor	p. 9
Vectors and Tensors	p. 10
Invariant Volume and Volume Integral	p. 16
Affine Connection - Parallel Transport	p. 17
Covariant Differentiation	p. 20
The Differential Equation of a Geodesic	p. 23
The Integrability of Parallel Displacement	p. 25
The Riemann-Christoffel Tensor	p. 28
The Bianchi Identity	p. 29
The Ricci Tensor and the Einstein Tensor	p. 29
The Weyl Tensor	p. 30
Geodesic Deviation	p. 32
Einstein's Field Equations	p. 35
Einstein's Formulation of the Field Equations	p. 35
Weak Field Approximation (Static Case)	p. 36
Gravitational Waves in Weak Field Approximation	p. 38
Detection of Gravitational Waves	p. 40
Integration of the Linearized Equations for a Stationary Axially Symmetric Distribution	p. 41
The Action Principle and the Energy-Momentum Tensors	p. 45
The Energy-Stress Tensor	p. 47
The Einstein Equations from the Variational Principle	p. 49
The Schwarzschild Metric and Crucial Tests	p. 52
The Schwarzschild Solution	p. 52
Birkhoff's Theorem	p. 54
Three Crucial Tests	p. 55
The PPN Formalism	p. 65
The Schwarzschild or the Spherically Symmetric Black Hole	p. 69
Frequency Shift of Spectral Lines of Light Emitted by a Collapsing/Exploding Spherical Body	p. 71
Fall in Apparent Luminosity of a Collapsing Body	p. 73
Kruskal-Szekeres Coordinates	p. 74
Historical Note on the Schwarzschild Black Hole	p. 76
Electromagnetism in General Relativity	p. 79
Introduction	p. 79
The Field of a Charged Particle	p. 80
Static Electrovac	p. 82
The Already Unified Field Theory	p. 83
Axially Symmetric Fields
The Lie Derivative and the Killing Equation	p. 87
Static and Stationary Metrics	p. 89
The Axially Symmetric Static Metric	p. 90
Weyl's Canonical Form	p. 91
The Case of Two Mass Particles	p. 93
The Schwarzschild Metric in the Form (6.21)	p. 95
Stationary Axisymmetric Vacuum Solutions	p. 96
The Kerr Metric or the Rotating Black Hole	p. 98
The Kerr Metric in Boyer-Lindquist Coordinates	p. 98
The Black Hole Property	p. 99
Locally Nonrotating Observers	p. 100
The Horizon as a Null Surface	p. 100
The Kerr-Newmann Metric	p. 102
The Penrose Process	p. 102
The Energy-Momentum Pseudotensor of the Gravitational Field and Loss of Energy by Gravitational Radiation	p. 105
The Pseudo-Energy-Momentum Tensor	p. 105
Historical Note	p. 107
Loss of Energy by Gravitational Radiation	p. 108
The Case of a Binary Star	p. 111
Analysis of the Observational Data of the Hulse- Taylor Pulsar. Confirmation of the Einstein Quadrupole Radiation Formula	p. 114
Relativistic Astrophysics	p. 121
White Dwarf Stars	p. 123
Introduction	p. 123
The Contraction of a Radiating Star in the Absence of Energy Generation	p. 123
Degeneracy and the Equation of State	p. 125
Limiting Mass for White Dwarfs	p. 128
A Simple Argument for the Mass Limit	p. 129
Critique of Chandrasekhar's Result and Later Works	p. 130
Historical Note	p. 131
Observational Data on White Dwarfs	p. 132
The Cooling and Age of White Dwarfs	p. 132
Stellar Evolution, Supernovae, and Compact Objects	p. 138
Introduction	p. 138
The Evolution of Stars	p. 138
The Dynamical Collapse	p. 140
Some Numerical Results	p. 141
Explosive Processes	p. 141
Supernova 1987 A	p. 143
Pulsars	p. 144
Introduction	p. 144
Distance from Dispersion Measure	p. 145
Identification of Pulsars as Neutron Stars	p. 147
The Energetics of Pulsar Emission	p. 148
The Magnetic Field at the Pulsar Surface	p. 149
The Age of Pulsars	p. 150
Calculation of the Braking Index	p. 150
The Nonvacuum Model	p. 151
Observational Determination of Pulsar Masses	p. 153
Cooling of Neutron Stars-Theory and Observation	p. 153
The Influence of Superfluidity	p. 155
The Influence of Pion Condensation	p. 155
The Influence of Quarks	p. 156
Spherically Symmetric Star Models	p. 159
Introduction	p. 159
The Tolman, Oppenheimer-Volkoff Equation	p. 160
The Equation of State for Cold Catalyzed Matter	p. 161
A Model of a Neutron Star and the Mass Limits	p. 164
The Problems of the Upper Mass Limit of Neutron Stars	p. 167
The Influence of Rotation, etc., on the Mass Limit	p. 171
Note on the Stability of Compact Objects	p. 172
Black Holes	p. 175
Introduction	p. 175
The No-Hair Theorem	p. 175
The Laws of Black Hole Physics	p. 177
Black Hole Thermodynamics	p. 178
The Identification of a Black Hole - Cygnus X-1	p. 180
The Possible Locale of the Occurrence of Black Holes	p. 183
The Quasi-Steller Objects (Quasars)	p. 184
Gravitational Lens	p. 185
Accretion onto Compact Objects	p. 192
Introduction - Spherically Symmetric Accretion	p. 192
Disk Accretion	p. 199
Compact X-Ray Sources	p. 203
Cosmology	p. 207
The Standard Cosmological Model	p. 209
Introduction to the Friedmann Metric	p. 209
Elementary Discussion of Standard Cosmology	p. 213
The Observational Background of Cosmology	p. 221
Summary	p. 226
The Singularity Problem	p. 228
Introduction	p. 228
The Raychaudhuri Equation	p. 228
The Meaning of Shear, Vorticity, and Expansion	p. 229
An Elementary Singularity Theorem	p. 230
The Godel Universe	p. 231
General Singularity Theorems	p. 232
Thermal History of the Universe - Cosmological Nucleosynthesis	p. 235
The Thermal History	p. 235
Cosmological Nucleosynthesis	p. 239
Structure Formation in the Universe	p. 243
The Problem	p. 243
The Linear Growth Formula	p. 244
Finite Perturbation	p. 249
Structure Formation with Dark Matter	p. 250
Grand Unified Theory and Spontaneous Symmetry Breaking	p. 253
Introduction	p. 253
Gauge Fields	p. 253
Weak Interaction	p. 254
Strong Interaction and Grand Unification	p. 255
Baryon Asymmetry and the Baryon/Photon Ratio	p. 260
The Inflationary Scenario	p. 264
Introduction	p. 264
The Problems in Terms of Entropy	p. 265
The Vacuum Energy-Stress Tensor and the de Sitter Phase	p. 266
The Different Models of Inflation	p. 267
A Critique of the Inflationary Models	p. 270
Fluctuations in the Inflationary Models	p. 270
Concluding Remarks	p. 275
Appendix. Differential Forms	p. 278
Introductory Ideas and Definitions	p. 278
Connection 1-Forms and Ricci Rotation Coefficients	p. 280
Cartan's Equations of Structure	p. 281
Bianchi Identities and Symmetry Properties of the Riemann-Christoffel Tensor	p. 282
An Example of the Calculation of the Riemann-Christoffel Tensor	p. 282
References	p. 285
Bibliography	p. 289
Index	p. 293
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