Nonlinear Generalised Functions in General Relativity

Abstract

In linear field theories distributions arise naturally in a number of different ways. They are used to describe idealised situations where the matter is confined to some lower dimensional submanifold – point particles, strings and shells of matter – they are used to describe junction conditions between matter and vacuum regions, and they are used in the description of shock waves. This chapter gives a brief introduction to the Colombeau algebras. Thus a non-linear generalised function is represented by a moderate sequence of smooth functions modulo a negligible sequence. The calculation of the energy-momentum tensor for the Kerr solution is significantly harder.