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

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dc.citation.issueNumber20en_US
dc.citation.volumeNumber27en_US
dc.contributor.authorGürses, M.en_US
dc.date.accessioned2016-02-08T09:56:24Z
dc.date.available2016-02-08T09:56:24Z
dc.date.issued2010en_US
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractKilling 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.en_US
dc.identifier.doi10.1088/0264-9381/27/20/205018en_US
dc.identifier.eissn1361-6382
dc.identifier.issn0264-9381
dc.identifier.urihttp://hdl.handle.net/11693/22167
dc.language.isoEnglishen_US
dc.publisherInstitute of Physics Publishing Ltd.en_US
dc.relation.isversionofhttp://dx.doi.org/10.1088/0264-9381/27/20/205018en_US
dc.source.titleClassical and Quantum Gravityen_US
dc.titleKilling vector fields in three dimensions: a method to solve massive gravity field equationsen_US
dc.typeArticleen_US
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