Distributional geometry in general relativity
Distributional geometry in general relativity
In this article we look at the extent to which one can use classical linear distributional geometry in general relativity. We then go on to look at a non-linear theory of distributional geometry based on Colombeau algebras and show that this is compatible with the linear theory in situations where both may be used. For both the linear and non-linear theories of distributional geometry we will use a geometric coordinate free description. We conclude by looking at the example of the thin string limit of solutions of the field equations for an infinite length gravitating straight cosmic string described by a complex scalar field coupled to a gauge field. We show that within the Colombeau algebra this has a well-defined energy-momentum tensor and curvature which are associated to classical distributions.
distributional geometry, colombeau algebras, general relativity, cosmic strings
692-705
Vickers, J.A.
719cd73f-c462-417d-a341-0b042db88634
March 2012
Vickers, J.A.
719cd73f-c462-417d-a341-0b042db88634
Abstract
In this article we look at the extent to which one can use classical linear distributional geometry in general relativity. We then go on to look at a non-linear theory of distributional geometry based on Colombeau algebras and show that this is compatible with the linear theory in situations where both may be used. For both the linear and non-linear theories of distributional geometry we will use a geometric coordinate free description. We conclude by looking at the example of the thin string limit of solutions of the field equations for an infinite length gravitating straight cosmic string described by a complex scalar field coupled to a gauge field. We show that within the Colombeau algebra this has a well-defined energy-momentum tensor and curvature which are associated to classical distributions.
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e-pub ahead of print date: 1 May 2011
Published date: March 2012
Keywords:
distributional geometry, colombeau algebras, general relativity, cosmic strings
Organisations:
Mathematical Sciences
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Local EPrints ID: 207997
URI: http://eprints.soton.ac.uk/id/eprint/207997
ISSN: 0393-0440
PURE UUID: cb9c24cf-69c2-44c3-a995-55a742c88bf5
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Date deposited: 16 Jan 2012 16:36
Last modified: 15 Mar 2024 02:34
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J.A. Vickers
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