Hidden Symmetries of Higher Dimensional Black Holes and Uniqueness of the Kerr-NUT-(A)dS spacetime
Krtouš, P.; Frolov, V. P.; Kubizňák, D.
We prove that the most general solution of the Einstein equations with the cosmological constant which admits a principal conformal Killing-Yano tensor is the Kerr-NUT-(A)dS metric. Even when the Einstein equations are not imposed, any spacetime admitting such hidden symmetry can be written in a canonical form which guarantees the following properties: it is of the Petrov type D, it allows the separation of variables for the Hamilton-Jacobi, Klein-Gordon, and Dirac equations, the geodesic motion in such a spacetime is completely integrable. These results naturally generalize the results obtained earlier in four dimensions.
type: | article |
journal: | Phys. Rev. D |
volume: | 78 |
pages: | 064022 |
year: | 2008 |
eprint: | arXiv:0804.4705 |
grants: | Exact solutions in higher dimensional and classical gravity, GAČR 202/08/0187; 2008-2011; hlavní řešitel: Jiří PodolskýCentrum teoretické astrofyziky, MŠMT ČR LC06014; 2005-2009; hlavní řešitel: Jiří Horáček |