General Relativity, Astrophysics, and Cosmology

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Springer Science & Business Media, 14 нояб. 2003 г. - Всего страниц: 312
For about half a century the general theory of relativity attracted little attention from physicists. However, the discovery of compact objects such as quasars and pulsars, as well as candidates for black holes on the one hand, and the microwave background radiation on the other hand completely changed the picture. In addition, developments in elementary particle physics, such as predictions of the behavior of matter at the ultrahigh energies that might have prevailed in the early stages of the big bang, have greatly en hanced the interest in general relativity. These developments created a large body of readers interested in general relativity, and its applications in astrophysics and cosmology. Having neither the time nor the inclination to delve deeply into the technical literature, such readers need a general introduction to the subject before exploring applica tions. It is for these readers that the present volume is intended. Keeping in mind the broad range of interests and wanting to avoid mathematical compli cations as much as possible, we have ventured to combine all three topics relativity, astrophysics, and cosmology-in a single volume. Naturally, we had to make a careful selection of topics to be discussed in order to keep the book to a manageable length.
 

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Содержание

1 Introduction
3
12 The Principle of Equivalence
4
Gravitational Redshift
6
14 A Fifth Force
8
2 Tensor Calculus and Riemannian Geometry
9
22 Vectors and Tensors
10
23 Invariant Volume and Volume Integral
16
24 Affine ConnectionParallel Transport
17
116 Supernova 1987 A
143
12 Pulsars
144
122 Distance from Dispersion Measure
145
123 Identification of Pulsars as Neutron Stars
147
124 The Energetics of Pulsar Emission
148
125 The Magnetic Field at the Pulsar Surface
149
126 The Age of Pulsars
150
128 The Nonvacuum Model
151

25 Covariant Differentiation
20
26 The Differential Equation of a Geodesic
23
27 The Integrability of Parallel Displacement
25
28 The RiemannChristoffel Tensor
28
29 The Bianchi Identity
29
211 The Weyl Tensor
30
212 Geodesic Deviation
32
3 Einsteins Field Equations
35
32 Weak Field Approximation Static Case
36
33 Gravitational Waves in Weak Field Approximation
38
34 Detection of Gravitational Waves
40
35 Integration of the Linearized Equations for a Stationary Axially Symmetric Distribution
41
36 The Action Principle and the EnergyMomentum Tensors
45
37 The EnergyStress Tensor
47
38 The Einstein Equations from the Variational Principle
49
4 The Schwarzschild Metric and Crucial Tests
52
42 Birkhoff s Theorem
54
43 Three Crucial Tests
55
44 The PPN Formalism
65
45 The Schwarzschild or the Spherically Symmetric Black Hole
69
46 Frequency Shift of Spectral Lines of Light Emitted by a CollapsingExploding Spherical Body
71
47 Fall in Apparent Luminosity of a Collapsing Body
73
48 KruskalSzekeres Coordinates
74
49 Historical Note on the Schwarzschild Black Hole
76
5 Electromagnetism in General Relativity
79
52 The Field of a Charged Particle
80
53 Static Electrovac
82
54 The Already Unified Field Theory
83
6 Axially Symmetric Fields
87
62 Static and Stationary Metrics
89
63 The Axially Symmetric Static Metric
90
64 Weyls Canonical Form
91
65 The Case of Two Mass Particles
93
66 The Schwarzschild Metric in the Form 621
95
67 Stationary Axisymmetric Vacuum Solutions Ernst 1968
96
7 The Kerr Metric or the Rotating Black Hole
98
72 The Black Hole Property
99
73 Locally Nonrotating Observers
100
75 The KerrNewmann Metric
102
8 The EnergyMomentum Pseudotensor of the Gravitational Field and Loss of Energy by Gravitational Radiation
105
82 Historical Note
107
83 Loss of Energy by Gravitational Radiation
108
84 The Case of a Binary Star
111
9 Analysis of the Observational Data of the HulseTaylor Pulsar Confirmation of the Einstein Quadrupole Radiation Formula
114
Relativistic Astrophysics
121
10 White Dwarf Stars
123
103 Degeneracy and the Equation of State
125
104 Limiting Mass for White Dwarfs
128
105 A Simple Argument for the Mass Limit
129
106 Critique of Chandrasekhars Result and Later Works
130
107 Historical Note
131
108 Observational Data on White Dwarfs
132
11 Stellar Evolution Supernovae and Compact Objects
138
113 The Dynamical Collapse
140
114 Some Numerical Results
141
129 Observational Determination of Pulsar Masses
153
1211 The Influence of Superfluidity
155
1213 The Influence of Quarks
156
13 Spherically Symmetric Star Models
159
132 The Tolman OppenheimerVolkoff Equation
160
133 The Equation of State for Cold Catalyzed Matter
161
134 A Model of a Neutron Star and the Mass Limits
164
135 The Problems of the Upper Mass Limit of Neutron Stars
167
136 The Influence of Rotation etc on the Mass Limit
171
137 Note on the Stability of Compact Objects
172
14 Black Holes
175
143 The Laws of Black Hole Physics
177
144 Black Hole Thermodynamics
178
145 The Identification of a Black HoleCygnus X1
180
146 The Possible Locale of the Occurrence of Black Holes
183
147 The QuasiStellar Objects Quasars
184
148 Gravitational Lens
185
15 Accretion onto Compact Objects
192
152 Disk Accretion
199
153 Compact XRay Sources
203
Part III Cosmology
207
16 The Standard Cosmological Model
209
162 Elementary Discussion of Standard Cosmology
213
163 The Observational Background of Cosmology
221
164 Summary
226
17 The Singularity Problem
228
173 The Meaning of Shear Vorticity and Expansion
229
174 An Elementary Singularity Theorem
230
175 The Godel Universe
231
176 General Singularity Theorems
232
18 Thermal History of the Universe Cosmological Nucleosynthesis
235
182 Cosmological Nucleosynthesis
239
19 Structure Formation in the Universe
243
192 The Linear Growth Formula
244
193 Finite Perturbation
249
194 Structure Formation with Dark Matter
250
20 Grand Unified Theory and Spontaneous Symmetry Breaking
253
203 Weak Interaction
254
204 Strong Interaction and Grand Unification
255
205 Baryon Asymmetry and the BaryonPhoton Ratio
260
21 The Inflationary Scenario
264
212 The Problems in Terms of Entropy
265
213 The Vacuum EnergyStress Tensor and the de Sitter Phase
266
214 The Different Models of Inflation
267
215 A Critique of the Inflationary Models
270
22 Concluding Remarks
275
Appendix Differential Forms
278
A2 Connection 1 Forms and Ricci Rotation Coefficients
280
A3 Cartans Equations of Structure
281
A4 Bianchi Identities and Symmetry Properties of the RiemannChristoffel Tensor
282
References
285
Bibliography
289
Index
293
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