Gravitational collapse and spacetime singularities

Pankaj S. Joshi0521871042, 9780521871044, 9780511378904

Physical phenomena in astrophysics and cosmology involve gravitational collapse in a fundamental way. The final fate of a massive star when it collapses under its own gravity at the end of its life cycle is one of the most important questions in gravitation theory and relativistic astrophysics, and is the foundation of black hole physics. General relativity predicts that continual gravitational collapse gives rise to a space-time singularity. Quantum gravity may take over in such regimes to resolve the classical space-time singularity. This book investigates these issues, and shows how the visible ultra-dense regions arise naturally and generically as an outcome of dynamical gravitational collapse. It will be of interest to graduate students and academic researchers in gravitation physics, fundamental physics, astrophysics, and cosmology. It includes a detailed review of recent research into gravitational collapse, and several examples of collapse models are investigated in detail.

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Table of contents :
Cover……Page 1
Half title……Page 3
Series title……Page 4
Title……Page 5
Copyright……Page 6
Dedication……Page 7
Contents……Page 9
Preface……Page 11
1 Introduction……Page 13
2.1 The manifold model……Page 22
2.1.1 Differentiable manifolds……Page 23
2.1.2 Vectors and one-forms……Page 25
2.1.3 Topological structure……Page 28
2.1.4 Tensors……Page 30
2.2 The metric tensor……Page 33
2.3 Connection……Page 36
2.4 Non-spacelike geodesics……Page 41
2.5 Spacetime curvature……Page 44
2.6 The Einstein equations……Page 50
2.7 Exact solutions……Page 55
2.7.1 Minkowski spacetime……Page 56
2.7.2 The ideal points boundary……Page 58
2.7.3 Conformal compactification……Page 59
2.7.4 Schwarzschild solution……Page 60
2.7.5 Homogeneous collapse and the blackhole……Page 64
2.7.6 Vaidya metric and the naked singularity……Page 68
3 Spherical collapse……Page 72
3.1 Basic framework……Page 74
3.2 Regularity conditions……Page 81
3.3 Collapsing matter clouds……Page 83
3.4 Nature of singularities……Page 91
3.5 Exterior geometry……Page 99
3.6 Dust collapse……Page 102
3.6.1 Tolman–Bondi–Lemaître (TBL) spacetimes……Page 104
3.6.2 Collapse endstates……Page 112
3.6.3 Structure of singularities……Page 117
3.6.4 Self-similar collapse……Page 118
3.6.5 Strength and global visibility……Page 123
3.6.6 Cosmological constant……Page 131
3.7 Equation of state……Page 141
4 Cosmic censorship……Page 147
4.1 Causal structure……Page 148
4.2 Spacetime singularities……Page 161
4.2.1 The definition of a singularity……Page 162
4.2.2 Gravitational focusing……Page 165
4.2.3 Existence of singularities……Page 171
4.3 Blackholes……Page 173
4.4 Higher spacetime dimensions……Page 181
4.5 Formulating the censorship……Page 187
1. A suitable energy condition must be obeyed…….Page 192
2. The collapse must develop from regular initial data…….Page 193
3. Singularities from realistic collapses must be gravitationally strong…….Page 194
4. The matter fields must be sufficiently general…….Page 195
5. The collapsing cloud must obey a realistic equation of state…….Page 196
6. All radiations from a naked singularity must be infinitely red-shifted…….Page 197
7. Will quantum gravity remove naked singularities?……Page 198
8. Should all naked singularities produced by matter fields be considered to be unphysical?……Page 199
9. Are naked singularities stable and generic?……Page 200
4.6 Genericity and stability……Page 202
4.6.1 Topology on the space of metrics……Page 204
4.6.2 Censorship and genericity issues……Page 205
4.6.3 Scalar field collapses……Page 214
4.6.4 Families of non-spacelike curves from a singularity……Page 215
5 Final fate of a massive star……Page 222
5.1 Life cycle of massive stars……Page 225
5.2 Evolution of a physically realistic collapse……Page 227
5.3 Non-spherical models……Page 237
5.4 Blackhole paradoxes……Page 247
5.5 Resolution of a naked singularity……Page 250
References……Page 267
Index……Page 281