  We prove that non-extremal black holes in four-dimensional general relativity
exhibit an infinite-dimensional symmetry in their near horizon region. By
prescribing a physically sensible set of boundary conditions at the horizon, we
derive the algebra of asymptotic Killing vectors, which is shown to be
infinite-dimensional and includes, in particular, two sets of supertranslations
and two mutually commuting copies of the Virasoro algebra. We define the
surface charges associated to the asymptotic diffeomorphisms that preserve the
boundary conditions and discuss the subtleties of this definition, such as the
integrability conditions and the correct definition of the Dirac brackets. When
evaluated on the stationary solutions, the only non-vanishing charges are the
zero-modes. One of them reproduces the Bekenstein-Hawking entropy of Kerr black
holes. We also study the extremal limit, recovering the NHEK geometry. In this
singular case, where the algebra of charges and the integrability conditions
get modified, we find that the computation of the zero-modes correctly
reproduces the black hole entropy. Furthermore, we analyze the case of three
spacetime dimensions, in which the integrability conditions notably simplify
and the field equations can be solved analytically to produce a family of exact
solutions that realize the boundary conditions explicitly. We examine other
features, such as the form of the algebra in the extremal limit and the
relation to other works in the literature.
