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      Gödel type metrics in three dimensions

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      Author
      Gürses, M.
      Date
      2010
      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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      102
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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.
      Keywords
      Einstein's equations in three dimensions
      Einstein-perfect fluid solutions
      Gödel type metrics
      Ricci and Cotton flows
      Topologically massive gravity
      Permalink
      http://hdl.handle.net/11693/22302
      Published Version (Please cite this version)
      http://dx.doi.org/10.1007/s10714-009-0914-7
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