2 - Exact and inexact solutions of the Einstein field equations

Summary

INTRODUCTION

There has been a tremendous growth in the understanding of General Relativity and of its relation to experiment in the past 30 years, resulting in its transformation from a subject in the doldrums on the periphery of theoretical physics, to a subject with a considerable experimental wing and and many recognised major theoretical achievements to its credit. The main areas of development have been,

1. * solar system tests of gravitational theories,

2. * gravitational radiation theory and detectors,

3. * black holes and gravitational collapse,

4. * cosmology and the dynamics of the early universe.

On the theoretical side, this development is based on understanding exact and inexact solutions of the Field Equations (the latter has three different meanings I will discuss later). In this brief review of theoretical developments, there is not space to give full references to all the original papers. Detailed references can be found in previous surveys, in particular ‘HE’ is Hawking and Ellis (1973), ‘TCE’ is Tipler Clarke and Ellis (1980), ‘HI’ is Hawking and Israel (1987), and ‘GR13’ is the proceedings of the 13th International meeting on General Relativity and Gravitation held in Cordoba, Argentina in 1992. Many of the issues raised here are considered at greater length elsewhere in this book, e.g. in the articles by MacCallum and Tod.