Higher-dimensional black holes: hidden symmetries and separation of variables

2008/02/29 by Valeri P. Frolov, Valeri P Frolov, David Kubiznak +1 · 2 citations
Physics and Astronomy · #Advanced Differential Geometry Research #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Black hole (networking) #Conformal map #Geodesic #Homogeneous space #Killing vector field #Separation of variables #Spacetime #Symmetry (geometry) #Tensor (intrinsic definition) #gr-qc #hep-th

paper · pdf · doi:10.1088/0264-9381/25/15/154005

published as Class.Quant.Grav.25:154005,2008 · 33 pages, no figures, updated references and corrected typos

arxiv created 2008/03/27 · openalex publication_date 2008/07/22 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

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.

Citations

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Cited by

• Motion of the charged test particles in Kerr-Newman-Taub-NUT spacetime and analytical solutions
• On the supersymmetric limit of Kerr-NUT-AdS metrics