Hidden Symmetries of Higher-Dimensional Black Hole Spacetimes

Abstract

The paper contains a brief review of recent results on hidden symmetries in higher dimensional black hole spacetimes. We show how the existence of a principal CKY tensor (that is a closed non-degenerate conformal Killing-Yano 2-form) allows one to generate a `tower' of Killing-Yano and Killing tensors responcible for hidden symmetries. These symmetries imply complete integrability of geodesic equations and the complete separation of variables in the Hamilton-Jacobi, Klein-Gordon and Dirac equations in the general Kerr-NUT-(A)dS metrics.

10 pages, Prepared for the Proceedings of the ICGA8 conference

Cited by in corpus (10)

• Hidden Symmetries of Dynamics in Classical and Quantum Physics
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• Closed conformal Killing-Yano tensor and uniqueness of generalized Kerr-NUT-de Sitter spacetime
• Dynamics of test particles in the general five-dimensional Myers-Perry spacetime
• Separability of the massive Dirac's equation in 5-dimensional Myers-Perry black hole geometry and its relation to a rank-three Killing-Yano tensor
• Parallel-propagated frame along null geodesics in higher-dimensional black hole spacetimes
• Symmetry operators and separability of massive Klein-Gordon and Dirac equations in the general 5-dimensional Kerr-(anti-)de Sitter black hole background
• Covariant Approach of the Dynamics of Particles in External Gauge Fields, Killing Tensors and Quantum Gravitational Anomalies
• Hidden Symmetries and Black Holes
• Higher-dimensional black holes with multiple equal rotations