The Analysis of Space-Time Singularities

by C. J. S. Clarke

Overview

The theorems of Hawking and Penrose show that space-times are likely to contain incomplete geodesics. Such geodesics are said to end at a singularity if it is impossible to continue the space-time and geodesic without violating the usual topological and smoothness conditions on the space-time. In this book the different possible singularities are defined, and the mathematical methods needed to extend the space-time are described in detail. The results obtained (many appearing here for the first time) show that singularities are associated with a lack of smoothness in the Riemann tensor. While the Friedmann singularity is analysed as an example, the emphasis is on general theorems and techniques rather than on the classification of particular exact solutions.

Product Details

ISBN-13:	9780521437967
Publisher:	Cambridge University Press
Publication date:	05/12/1994
Series:	Cambridge Lecture Notes in Physics , #1
Pages:	192
Product dimensions:	6.06(w) x 9.06(h) x 0.59(d)

Table of Contents

1. Introductory; 2. The Riemann tensor; 3. Boundary constructions; 4. Existence theory and differentiability; 5. The analytic extension problem; 6. Attributes of singularities; 7. Extension theories.

Editorial Reviews

"...will surely be extremely useful to researchers already working on cosmic censorship. or contemplating entering the field, and of great interest to classical relativists who are interested in finding out more about it." Robert J. Low, Mathematical Reviews

From the Publisher