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The use of generalised functions and distributions in general relativity

The use of generalised functions and distributions in general relativity
The use of generalised functions and distributions in general relativity
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 generalized 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.
0264-9381
R91-R114
Steinbauer, R.
03564261-185d-4e1d-97ed-a7633d552a34
Vickers, J.A.
719cd73f-c462-417d-a341-0b042db88634
Steinbauer, R.
03564261-185d-4e1d-97ed-a7633d552a34
Vickers, J.A.
719cd73f-c462-417d-a341-0b042db88634

Steinbauer, R. and Vickers, J.A. (2006) The use of generalised functions and distributions in general relativity. Classical and Quantum Gravity, 23 (10), R91-R114. (doi:10.1088/0264-9381/23/10/R01).

Record type: Article

Abstract

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 generalized 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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Published date: May 2006

Identifiers

Local EPrints ID: 29339
URI: http://eprints.soton.ac.uk/id/eprint/29339
ISSN: 0264-9381
PURE UUID: 25bbc9b6-1913-413e-8529-44d77326bac9
ORCID for J.A. Vickers: ORCID iD orcid.org/0000-0002-1531-6273

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Date deposited: 11 May 2006
Last modified: 28 Apr 2022 01:32

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Contributors

Author: R. Steinbauer
Author: J.A. Vickers ORCID iD

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