The use of Generalised Functions and Distributions in General Relativity

Details The use of Generalised Functions and Distributions in General Relativity The use of Generalised Functions and Distributions in General Relativity

2006-03-20

arxiv.org/abs/gr-qc/0603078v2

Class.Quant.Grav. 23 (2006) R91-R114

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex, 30 pages, final version, one reference added, to appear as topical review in Class. Quantum Grav

Scientific paper

10.1088/0264-9381/23/10/R01

In this paper we review the extent to which one can use classical distribution theory in describing solutions of Einstein's equations. We show that there are a number of physically interesting cases which cannot be treated using distribution theory but require a more general concept. We describe a mathematical theory of nonlinear generalised functions based on Colombeau algebras and show how this may be applied in general relativity. We end by discussing the concept of singularity in general relativity and show that certain solutions with weak singularities may be regarded as distributional solutions of Einstein's equations.

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