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      Killing vector fields in three dimensions: a method to solve massive gravity field equations

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      Author
      Gürses, M.
      Date
      2010
      Source Title
      Classical and Quantum Gravity
      Print ISSN
      0264-9381
      Electronic ISSN
      1361-6382
      Publisher
      Institute of Physics Publishing Ltd.
      Volume
      27
      Issue
      20
      Language
      English
      Type
      Article
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      Abstract
      Killing vector fields in three dimensions play an important role in the construction of the related spacetime geometry. In this work we show that when a three-dimensional geometry admits a Killing vector field then the Ricci tensor of the geometry is determined in terms of the Killing vector field and its scalars. In this way we can generate all products and covariant derivatives at any order of the Ricci tensor. Using this property we give ways to solve the field equations of topologically massive gravity (TMG) and new massive gravity (NMG) introduced recently. In particular when the scalars of the Killing vector field (timelike, spacelike and null cases) are constants then all three-dimensional symmetric tensors of the geometry, the Ricci and Einstein tensors, their covariant derivatives at all orders, and their products of all orders are completely determined by the Killing vector field and the metric. Hence, the corresponding three-dimensional metrics are strong candidates for solving all higher derivative gravitational field equations in three dimensions. © 2010 IOP Publishing Ltd.
      Permalink
      http://hdl.handle.net/11693/22167
      Published Version (Please cite this version)
      http://dx.doi.org/10.1088/0264-9381/27/20/205018
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