Congruences of World Lines

Abstract

Material particles and photons are of paramount importance in constructing and analysing models of gravitational fields in general relativity. Their histories in space-time are congruences of time-like and light-like (or null) world lines respectively. Material particles and photons therefore play a central role in this book and we begin by describing the standard theory of congruences of time-like world lines and of null congruences. In the light-like case we shall only require a knowledge of null geodesic congruences. For use later we describe geodesic deviation equations with the help of Synge’s world function and parallel propagator.