We show that the asymptotic symmetries close to nonextremal black hole horizons are generated by an extension of supertranslations. This group is generated by a semidirect sum of Virasoro and Abelian currents. The charges associated with the asymptotic Killing symmetries satisfy the same algebra. When considering the special case of a stationary black hole, the zero mode charges correspond to the angular momentum and the entropy at the horizon.

The four-dimensional S-matrix is reconsidered as a correlator on the celestial sphere at null infinity. Asymptotic particle states can be characterized by the point at which they enter or exit the celestial sphere as well as their SL(2, C) Lorentz quantum numbers: namely their conformal scaling dimension and spin h±h instead of the energy and momentum. This characterization precludes the notion of a soft particle whose energy is taken to zero. We propose it should be replaced by the notion of a conformally soft particle with h = 0 orh = 0. For photons we explicitly construct conformally soft SL(2, C) currents with dimensions (1, 0) and identify them with the generator of a U (1) Kac-Moody symmetry on the celestial sphere. For gravity the generator of celestial conformal symmetry is constructed from a (2, 0) SL(2, C) primary wavefunction. Interestingly, BMS supertranslations are generated by a spin-one weight ( 3 2 , 1 2 ) operator, which nevertheless shares holomorphic characteristics of a conformally soft operator. This is because the right hand side of its OPE with a weight (h,h) operator O h,h involves the shifted operator O h+ 1 2 ,h+ 1 2 . This OPE relation looks quite unusual from the celestial CFT 2 perspective but is equivalent to the leading soft graviton theorem and may usefully constrain celestial correlators in quantum gravity.

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 Witt 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.