## General Relativity, Astrophysics, and CosmologySpringer Science & Business Media, 14. nóv. 2003 - 312 síður 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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### Efni

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 |

285 | |

Bibliography | 289 |

293 | |

### Aðrar útgáfur - View all

General Relativity, Astrophysics, and Cosmology A.K. Raychaudhuri,S. Banerji,A. Banerjee Engin sýnishorn í boði - 1992 |

### Common terms and phrases

accretion angular appear assume baryon becomes black hole calculation called compact components condition consider constant coordinate corresponding Cosmology defined density derivative determined differential direction distance distribution effect Einstein electromagnetic electrons emission energy equation equilibrium expression factor fall field field equations Figure formula function galaxies geodesic geometry given gives gravitational field Hence horizon idea increase indicate integration interaction introduce involve leads light limit mass matter metric momentum motion neutron star Note null vector object observed obtain occur particles period perturbation physics possible potential present principle Problems pulsar radiation redshift reduces region relation relativity respectively result rotation scalar Schwarzschild singularity situation solution space spherical surface symmetric temperature tensor term theory tion transformation universe vanish vector velocity wave white dwarfs μν

### Tilvísanir í bókina

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Applied Functional Analysis: Main Principles and Their Applications Eberhard Zeidler Takmarkað sýnishorn - 1995 |