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The induced geometry at black hole horizons satisfies equations that have consequences similar to those known from global black hole theory: the preferred spherical topology of horizon cross sections - "topological censorship", the existence of axial symmetry - "rigidity", the solution space parametrized by few parameters - "no hair". One of these equations, which knows the secrets of black holes, follows from the Petrov type D of the Weyl tensor on the horizon. For extreme horizons, these equations take a stronger form. There are still important open problems related to the existence of solutions. The class of Petrov type D spacetimes, which are solutions of the Einstein equations, is characterized by a nonzero NUT parameter. In this case, a certain pair of Killing vectors is distinguished by properties of the geometry of the space of orbits. This observation leads to the construction of a globally defined Kerr-NUT-(A)-de-Sitter spacetimes free of the conical singularity. It may be also considered in the acceperated Kerr-NUT-(A)-de-Sitter case.
