Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-02-04
Class.Quant.Grav.25:154005,2008
Physics
High Energy Physics
High Energy Physics - Theory
33 pages, no figures, updated references and corrected typos
Scientific paper
10.1088/0264-9381/25/15/154005
In this paper, we discuss hidden symmetries in rotating black hole spacetimes. We start with an extended introduction which mainly summarizes results on hidden symmetries in four dimensions and introduces Killing and Killing-Yano tensors, objects responsible for hidden symmetries. We also demonstrate how starting with a principal CKY tensor (that is a closed non-degenerate conformal Killing-Yano 2-form) in 4D flat spacetime one can "generate" 4D Kerr-NUT-(A)dS solution and its hidden symmetries. After this we consider higher-dimensional Kerr-NUT-(A)dS metrics and demonstrate that they possess a principal CKY tensor which allows one to generate the whole tower of Killing-Yano and Killing tensors. These symmetries imply complete integrability of geodesic equations and complete separation of variables for the Hamilton-Jacobi, Klein-Gordon, and Dirac equations in the general Kerr-NUT-(A)dS metrics.
Frolov Valeri P.
Kubiznak David
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