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.
R91-R114
Steinbauer, R.
03564261-185d-4e1d-97ed-a7633d552a34
Vickers, J.A.
719cd73f-c462-417d-a341-0b042db88634
May 2006
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), .
(doi:10.1088/0264-9381/23/10/R01).
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
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Local EPrints ID: 29339
URI: http://eprints.soton.ac.uk/id/eprint/29339
ISSN: 0264-9381
PURE UUID: 25bbc9b6-1913-413e-8529-44d77326bac9
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Date deposited: 11 May 2006
Last modified: 16 Mar 2024 02:34
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Author:
R. Steinbauer
Author:
J.A. Vickers
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