Hernán A. González

TL;DR: It is shown that the asymptotic symmetries close to nonextremal black hole horizons are generated by an extension of supertranslations, generated by a semidirect sum of Virasoro and Abelian currents.

TL;DR: In this paper, the authors analyzed the relation between asymptotically anti-de Sitter and spacetimes in 3D space and showed that the limit of vanishing cosmological constant cannot be naively taken in standard Fefferman-Graham coordinates.

Abstract: 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.

TL;DR: In this paper, a consistent set of asymptotic conditions for higher spin gravity in three dimensions is proposed in the case of vanishing cosmological constant, and the results are found to be spanned by a higher spin extension of the BMS3 algebra with an appropriate central extension.

TL;DR: In this paper, the coupling constants of the Hamiltonian formulation of Liouville theory were taken into account to construct a two-dimensional invariant field theory that is likely to control the boundary dynamics at null infinity of threedimensional asymptotically flat gravity.