The Large Scale Structure Of Space-Time

The subject of this book is the structure of space-time on lengthscales from 10-13 em, the radius of an elementary particle, up to
1028 em, the radius of the universe. For reasons explained in
chapters 1 and 3, we base our treatment on Einstein’s General
Theory of Relativity. This theory leads to two remarkable predictions about the universe: first, that the final fate of massive
stars is to collapse behind an event horizon to form a ‘black hole’
which will contain a singula.rity; and secondly, that there is a
singularity in our past which constitutes, in some sense, a beginning to the universe. Our discussion is principally aimed at developing
these two results. They depend primarily on two areas ofstudy: first,
the theory of the behaviour of families of timelike and null curves in
space-time, and secondly, the study of the nature of the various
causal relations in any space-time. We consider these subjects in
detail. In addition we develop the theory of the time-development
of solutions of Einstein’s equations from given initial data. The ·discussion is supplemented by an examination of global properties of
a variety of exact solutions of Einstein’s field equations, many of
which show some rather unexpected behaviour.
This book is based in part on an Adams Prize Essay by one of us
(S. W. H.). Many of the ideas presented here are due to R. Penrose
and R. P. Geroch, and we thank them for their help. We would refer
our readers to their review articles in the Battelle Rencontres (Penrose
(196R)), Midwest Relativity Conference Report (Geroch (1970c)),
Varcnna Summer School Proceedings (Geroch (1971)), and Pittsburgh
Conference Report (Penrose (1972b)). We have benefited from discussions and suggestions from many of our colleagues, particularly
B. Carter and D. W. Sciama. Our thanks are due to them also.