## Gravitational Collapse and Spacetime SingularitiesPhysical 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 research into gravitational collapse, and several examples of collapse models are investigated in detail. |

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### Contents

1 | |

2 The spacetime manifold | 10 |

3 Spherical collapse | 60 |

4 Cosmic censorship | 135 |

5 Final fate of a massive star | 210 |

255 | |

269 | |

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### Common terms and phrases

apparent horizon blackhole blackhole physics boundary Cauchy surface causal structure central singularity collapse endstate collapse models collapse scenarios collapsing cloud comoving coordinate components conﬁguration continual collapse coordinate cosmic censorship hypothesis curvature singularity deﬁned deﬁnition density proﬁle develops diﬀerent diﬀerentiable discussed dust cloud dust collapse Einstein equations energy density event horizon example existence exterior ﬁnal fate ﬁnite ﬁrst formation future directed geometry given globally hyperbolic gravitational collapse gravity regions hypersurface implies inﬁnity inhomogeneous initial density manifold mass function massive star matter cloud matter ﬁelds metric tensor Minkowski spacetime naked singularity non-spacelike curves non-spacelike geodesics non-zero null geodesics perfect ﬂuids possible pressure quantum gravity radius Riemann tensor satisﬁed scalar ﬁeld Schwarzschild shear shells singularity curve solution spacelike spacetime singularity speciﬁc spherically symmetric strong curvature singularity tangent theory timelike curve timelike geodesics trajectories trapped surfaces Vaidya vanish vector velocity visible well-deﬁned