Visibility of spacetime singularities formed in the gravitational collapse of a star has been one of the most disputed topics of modern astrophysics and cosmology for the past four decades. This provocative, topical book presents the scientific foundation for thinking that spacetime singularities formed in the collapse of a star might be visible. The book portrays methods for determining the nature of singularities arising in four and higher dimensional spacetimes. It is the most comprehensive book, which will be an essential reading for astrophysicists, cosmologists and all those interested in understanding the gravitational collapse of a star.

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 research into gravitational collapse, and several examples of collapse models are investigated in detail.

The generality of the formalism is elucidated in the final chapters of the thesis by looking at the coupling of both electromagnetism and scalar fields in the collapse models. The coupling of electromagnetism to general relativity is given by the Einstein-Maxwell equations, and we are therefore describing relativistic plasma physics. We give a covariant formulation of these plasma equations in 3 + 1 form and discuss the analogues of these equations in standard Newtonian plasma physics. The reduction of these equations to the spherically symmetric case is given in detail along with a further reduction to both the charged Vaidya spacetime in non-null coordinates and the Reissner-Nordström spacetime. Again, all regions of this spacetime are expressed in a single coordinate system and an initial value formalism for a collapsing charged fluid is discussed analogously to the non-electromagnetic case. The final chapter discusses the advantage of this formalism in the context of the gravitational collapse of non-spherical spacetimes. The simplest non-spherical spacetimes which emits gravitational radiation are the vacuum Robinson-Trautman spacetimes. However, generalizations of these spacetimes to include matter are not known. This final chapter is for the most part qualitative, and concentrates on providing causality to outgoing Robinson-Trautman spacetimes. We make significant progress in understanding this problem by establishing the Einstein field equations in intial value form for non-spherical spacetimes which include matter sources.

In this thesis, I first review the fundamentals of Einstein's theory of gravity in four-dimensional spacetimes, and then develop the general formulas of thin shells in this theory. Applying these formulas to spherically symmetric thin shells, I study the gravitational collapse of dust clouds in the background of dark energy. To solve the relevant equations, I develop a computer program, and investigate four representative cases, in which one is without dark energy and the others are with. I find that in all the four cases black holes can be formed from the gravitational collapse of the dust cloud.

Proceedings of IAU Symposium No. 64, Warsaw, Poland, September 5-8, 1973

A comprehensive book for the post graduates and researchers in theoretical astrophysics who want to study the space-time singularities arising in the gravitational collapse from a mathematician s point of view. The study has become significant from the perspective of cosmic censorship hypothesis. Four and higher-dimensional space-times are investigated for the possibility of cosmic censorship violation. Analysis of space-time singularities formed in the gravitational collapse of a star is one of the most important areas of mathematical research today. The book provides methods to determine the stability and strength of the singularities arising in various space-times.