Abstract

The 4D rotating black hole described by the Kerr geometry possesses many of what was called by Chandrasekhar “miraculous” properties. Most of them can be related to the existence of a fundamental hidden symmetry called the principal conformal Killing-Yano (PCKY) tensor. In my talk I shall demonstrate that, in this context, four dimensions are not exceptional and that the (spherical horizon topology) higher-dimensional rotating black holes are very similar to their four-dimensional cousins. Namely, I shall present the most general spacetime admitting the PCKY tensor and show that is possesses the following properties: 1) It is of the algebraic type~D of the higher-dimensional algebraic classification. 2) It allows a separation of variables for the Hamilton—Jacobi, Klein—Gordon, Dirac, and stationary string equations. 3) The geodesic motion in such a spacetime is completely integrable. The problem of finding parallel-propagated frames reduces to the set of the first order ordinary differential equations. 4) When the Einstein equations with the cosmological constant are imposed the metric becomes the Kerr-NUT-(A)dS spacetime.