Gödel type metrics in three dimensions

Date
2010
Authors
Gürses, M.
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Source Title
General Relativity and Gravitation
Print ISSN
0001-7701
Electronic ISSN
1572-9532
Publisher
Springer New York LLC
Volume
42
Issue
6
Pages
1413 - 1426 -
Language
English
Type
Article
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Abstract

We show that the Gödel type metrics in three dimensions with arbitrary two dimensional background space satisfy the Einstein-perfect fluid field equations. We also show that there exists only one first order partial differential equation satisfied by the components of fluid's velocity vector field. We then show that the same metrics solve the field equations of the topologically massive gravity where the two dimensional background geometry is a space of constant negative Gaussian curvature. We discuss the possibility that the Gödel type metrics to solve the Ricci and Cotton flow equations. When the vector field uμ is a Killing vector field, we came to the conclusion that the stationary Gödel type metrics solve the field equations of the most possible gravitational field equations where the interaction lagrangian is an arbitrary function of the electromagnetic field and the curvature tensors. © 2009 Springer Science+Business Media, LLC.

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Keywords
Einstein's equations in three dimensions, Einstein-perfect fluid solutions, Gödel type metrics, Ricci and Cotton flows, Topologically massive gravity
Citation
Published Version (Please cite this version)