Conformal Mappings in Relativistic Astrophysics

Conformal Mappings in Relativistic Astrophysics

We describe the use of conformal mappings as a mathematical mechanism to obtain exact solutions of the Einstein field equations in general relativity. The behaviour of the spacetime geometry quantities is given under a conformal transformation, and the Einstein field equations are exhibited for a pe...

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Main Authors: S. Hansraj, K. S. Govinder, N. Mewalal
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/196385
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spelling doaj-b6d2fc0bf0994dcf936425cc453a548f2020-11-24T23:04:17ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/196385196385Conformal Mappings in Relativistic AstrophysicsS. Hansraj0K. S. Govinder1N. Mewalal2Astrophysics and Cosmology Research Unit, School of Mathematics, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South AfricaAstrophysics and Cosmology Research Unit, School of Mathematics, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South AfricaAstrophysics and Cosmology Research Unit, School of Mathematics, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South AfricaWe describe the use of conformal mappings as a mathematical mechanism to obtain exact solutions of the Einstein field equations in general relativity. The behaviour of the spacetime geometry quantities is given under a conformal transformation, and the Einstein field equations are exhibited for a perfect fluid distribution matter configuration. The field equations are simplified and then exact static and nonstatic solutions are found. We investigate the solutions as candidates to represent realistic distributions of matter. In particular, we consider the positive definiteness of the energy density and pressure and the causality criterion, as well as the existence of a vanishing pressure hypersurface to mark the boundary of the astrophysical fluid.http://dx.doi.org/10.1155/2013/196385
collection DOAJ
language English
format Article
sources DOAJ
author S. Hansraj
K. S. Govinder
N. Mewalal
spellingShingle S. Hansraj
K. S. Govinder
N. Mewalal
Conformal Mappings in Relativistic Astrophysics
Journal of Applied Mathematics
author_facet S. Hansraj
K. S. Govinder
N. Mewalal
author_sort S. Hansraj
title Conformal Mappings in Relativistic Astrophysics
title_short Conformal Mappings in Relativistic Astrophysics
title_full Conformal Mappings in Relativistic Astrophysics
title_fullStr Conformal Mappings in Relativistic Astrophysics
title_full_unstemmed Conformal Mappings in Relativistic Astrophysics
title_sort conformal mappings in relativistic astrophysics
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2013-01-01
description We describe the use of conformal mappings as a mathematical mechanism to obtain exact solutions of the Einstein field equations in general relativity. The behaviour of the spacetime geometry quantities is given under a conformal transformation, and the Einstein field equations are exhibited for a perfect fluid distribution matter configuration. The field equations are simplified and then exact static and nonstatic solutions are found. We investigate the solutions as candidates to represent realistic distributions of matter. In particular, we consider the positive definiteness of the energy density and pressure and the causality criterion, as well as the existence of a vanishing pressure hypersurface to mark the boundary of the astrophysical fluid.
url http://dx.doi.org/10.1155/2013/196385
work_keys_str_mv AT shansraj conformalmappingsinrelativisticastrophysics
AT ksgovinder conformalmappingsinrelativisticastrophysics
AT nmewalal conformalmappingsinrelativisticastrophysics
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