Gravitational Collapse And Spacetime Singularities

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, first published in 2007, 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 physics of black holes and spacetime singularities is now a well established area of research in gravitation theory. Over recent years researchers have begun to study the internal structure of black holes and spacetime singularities. This book is primarily the proceedings of a workshop devoted to the subject. The chapters are mainly written versions of the talks given at the workshop. However, the authors have written extended introductions to their contributions, so that a reader, well versed in gravitation theory, but unaware of the current research in this subfield, should be able to follow the text Several topics are considered by more than one author, bringing into the text different viewpoints on these topics. As a result, this book is suitable for graduate students who wish to familiarize themselves with the various aspects of the structure of black holes, and for researchers who wish to learn about advances in subfields other than their own. Topics covered include: the nature of thesingularities (both null and spacelike) and the spacetime inside black holes coupled to various matter fields in classical and semiclassical gravity, as well as in alternative gravity theories; the cosmic censorship hypothesis and its connection to black hole interiors; cosmological singularities and their relation with black hole singularities; and black hole entropy and evaporation.

Black holes are one of the most fascinating predictions of general relativity. They are the natural product of the complete gravitational collapse of matter and today we have a body of observational evidence supporting the existence of black holes in the Universe. However, general relativity predicts that at the center of black holes there are spacetime singularities, where predictability is lost and standard physics breaks down. It is widely believed that spacetime singularities are a symptom of the limitations of general relativity and must be solved within a theory of quantum gravity. Since we do not have yet any mature and reliable candidate for a quantum gravity theory, researchers have studied toy-models of singularity-free black holes and of singularity-free gravitational collapses in order to explore possible implications of the yet unknown theory of quantum gravity. This book reviews all main models of regular black holes and non-singular gravitational collapses proposed in the literature, and discuss the theoretical and observational implications of these scenarios.

Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.

An accessible introductory textbook on general relativity, covering the theory's foundations, mathematical formalism and major applications.

This book journeys into one of the most fascinating intellectual adventures of recent decades - understanding and exploring the final fate of massive collapsing stars in the universe. The issue is of great interest in fundamental physics and cosmology today, from both the perspective of gravitation theory and of modern astrophysical observations. This is a revolution in the making and may be intimately connected to our search for a unified understanding of the basic forces of nature, namely gravity that governs the cosmological universe, and the microscopic forces that include quantum phenomena. According to the general theory of relativity, a massive star that collapses catastrophically under its own gravity when it runs out of its internal nuclear fuel must give rise to a space-time singularity. Such singularities are regions in the universe where all physical quantities take their extreme values and become arbitrarily large. The singularities may be covered within a black hole, or visible to faraway observers in the universe. Thus, the final fate of a collapsing massive star is either a black hole or a visible naked singularity. We discuss here recent results and developments on the gravitational collapse of massive stars and possible observational implications when naked singularities happen in the universe. Large collapsing massive stars and the resulting space-time singularities may even provide a laboratory in the cosmos where one could test the unification possibilities of basic forces of nature.

This textbook provides an introduction to general relativity for mathematics undergraduates or graduate physicists. After a review of Cartesian tensor notation and special relativity the concepts of Riemannian differential geometry are introducted. More emphasis is placed on an intuitive grasp of the subject and a calculational facility than on a rigorous mathematical exposition. General relativity is then presented as a relativistic theory of gravity reducing in the appropriate limits to Newtonian gravity or special relativity. The Schwarzchild solution is derived and the gravitational red-shift, time dilation and classic tests of general relativity are discussed. There is a brief account of gravitational collapse and black holes based on the extended Schwarzchild solution. Other vacuum solutions are described, motivated by their counterparts in linearised general relativity. The book ends with chapters on cosmological solutions to the field equations. There are exercises attached to each chapter, some of which extend the development given in the text.