Closed conformal Killing-Yano tensor and uniqueness of generalized Kerr-NUT-de Sitter spacetime

Abstract

The higher-dimensional Kerr-NUT-de Sitter spacetime describes the general rotating asymptotically de Sitter black hole with NUT parameters. It is known that such a spacetime possesses a rank-2 closed conformal Killing-Yano (CKY) tensor as a ``hidden'' symmetry which provides the separation of variables for the geodesic equations and Klein-Gordon equations. We present a classification of higher-dimensional spacetimes admitting a rank-2 closed CKY tensor. This provides a generalization of the Kerr-NUT-de Sitter spacetime. In particular, we show that the Kerr-NUT-de Sitter spacetime is the only spacetime with a non-degenerate CKY tensor.

24 pages, LaTeX; v2: references added, published version

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• Generalized Killing-Yano equations in D=5 gauged supergravity
• Killing-Yano tensors and some applications
• Separability of Gravitational Perturbation in Generalized Kerr-NUT-de Sitter Spacetime
• Quasinormal modes of Proca fields in a Schwarzschild-AdS spacetime
• Geodesics and Symmetries of Doubly-Spinning Black Rings
• Hidden symmetries of Eisenhart-Duval lift metrics and the Dirac equation with flux
• Local metrics admitting a principal Killing-Yano tensor with torsion
• Symmetry operators and separability of massive Klein-Gordon and Dirac equations in the general 5-dimensional Kerr-(anti-)de Sitter black hole background
• A simple test for spacetime symmetry
• Excitations of the Myers-Perry Black Holes
• Integrability Conditions for Killing-Yano Tensors and Conformal Killing-Yano Tensors
• General Wahlquist Metrics in All Dimensions
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• Spacetimes with a separable Klein-Gordon equation in higher dimensions
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• No more CKY two-forms in the NHEK
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• Maximal Analytic Extension and Hidden Symmetries of the Dipole Black Ring
• Spacetime characterizations of $\Lambda$-vacuum metrics with a null Killing 2-form
• Applications of hidden symmetries to black hole physics
• Homogeneous Symmetry Operators in Kerr--NUT--AdS Spacetimes