First published in 1973, this influential work discusses Einstein's General Theory of Relativity to show how two of its predictions arise: first, that the ultimate fate of many massive stars is to undergo gravitational collapse to form 'black holes'; and second, that there was a singularity in the past at the beginning of the universe. Starting with a precise formulation of the theory, including the necessary differential geometry, the authors discuss the significance of space time curvature and examine the properties of a number of exact solutions of Einstein's field equations. They develop the theory of the causal structure of a general space time. use it to prove a number of theorems establishing the inevitability of singularities under certain conditions. A Foreword contributed by Abhay Ashtekar and a new Preface from George Ellis help put the volume into context of the developments in the field over the past fifty years.

Table of Contents

1. The role of gravity

2. Differential geometry

3. General relativity

4. The physical significance of curvature

5. Exact solutions

6. Causal structure

7. The Cauchy problem in General Relativity

8. Space-time singularities

9. Gravitational collapse and black holes

10. The initial singularity in the universe

Appendix A: Translation of an essay by Peter Simon Laplace

Appendix B: Spherically symmetric solutions and Birkhoff’s theorem

About the Authors

Stephen W. Hawking (1942–2018) was an English theoretical physicist, cosmologist and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge. He was the Lucasian Professor of Mathematics at Cambridge from 1979 to 2009 and is the author of numerous books, including the international best-seller A Brief History of Time. (1989).

George F. R. Ellis is the emeritus distinguished professor of complex systems in the Department of Mathematics and Applied Mathematics at the University of Cape Town, South Africa. He is considered one of the world's leading theorists in cosmology and, in recent years, he has been prolific in areas relating to the philosophy of science. He is author or co-author of more than a dozen books, including Relativistic Cosmology (with Roy Maartens and Malcolm MacCallum, 2012).