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Nontrivial diffeomorphisms act on the horizon of a generic 4D black holes and create distinguishing features referred to as soft hair. Amongst these are a leftâ€"right pair of Virasoro algebras with associated charges that reproduce the Bekensteinâ€"Hawking entropy for Kerr black holes. In this paper we show that if one adds a negative cosmological constant, there is a similar set of infinitesimal diffeomorphisms that act non-trivially on the horizon. The algebra of these diffeomorphisms gives rise to a central charge. Adding a boundary counterterm, justified to achieve integrability, leads to well-defined central charges with c L = c R. The macroscopic area law for Kerr-AdS black holes follows from the assumption of a Cardy formula governing the black hole microstates. [ABSTRACT FROM AUTHOR]

A new solution of four-dimensional vacuum General Relativity is presented. It describes the near horizon region of the extreme (maximally spinning) binary black hole system with two identical extreme Kerr black holes held in equilibrium by a massless strut. This is the first example of a non-supersymmetric, near horizon extreme binary black hole geometry of two uncharged black holes. The black holes are co-rotating, their relative distance is fixed, and the solution is uniquely specified by the mass. Asymptotically, the geometry corresponds to the near horizon extreme Kerr (NHEK) black hole. The binary extreme system has finite entropy. [ABSTRACT FROM AUTHOR]