Black holes, hidden symmetry and complete integrability: Brief Review
arXiv:1210.7115
Abstract
This paper contains a brief review of the remarkable properties of higher dimensional rotating black holes with the spherical topology of the horizon. We demonstrate that these properties are connected with and generated by a special geometrical object, the Principal Conformal Killing-Yano tensor (PCKYT). The most general solution, describing such black holes, Kerr-NUT-ADS metric, admits this structure. Moreover a solution of the Einstein Equations with (or without) a cosmological constant which possesses PCKYT is the Kerr-NUT-ADS metric. This object (PCKYT) is responsible for such remarkable properties of higher dimensional rotating black holes as: (i) complete integrability of geodesic equations and (ii) complete separation of variables of the important field equations.
Brief version of the talk presented at the Conference: "Relativity and Gravitation: 100 years after Einstein in Prague", Prague, 25-29 June, 2012. Prepared for the Proceedings of this conference