Extended symmetries at the black hole horizon

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.

Near-horizon BMS symmetries as fluid symmetries

“…This matches the near-horizon BMS charge algebra of Donnay et al [39] (for a certain choice of boundary conditions). The relationship with fluid dynamics provides a physical interpretation for the charges, which may be useful for understanding asymptotic symmetries in more general situations.…”

Black hole evaporation, quantum hair and supertranslations

“…This approach has received widespread attention (see e.g. [13][14][15][16][17][18][19][20][21][22][23][24]). In particular, a potential new form of classical hair for a black hole has been proposed [25,26].…”

“…In this case, the memory effect the ingoing wave causes, parameterized by T − , is exactly canceled by the memory effect of the outgoing wave, parameterized by T + , so that there is no overall memory effect after the process. In that case, if we match T − and T + at each angle as in (23), it is possible to simply describe the overall memory effect as T − + T + .…”

“…As explained in Sect. 2.2, we employ the angle-wise matching (23). Thus, we obtain the static final state of the planet:…”

Quantum memory for Rindler supertranslations

“…For a Rindler horizon, the notion of supertranslation hair has been characterized in [19][20][21][22] (for a related discussion see [23]). It was shown in [24] that the Rindler horizon can be implanted with supertranslation hair by letting a shock wave without planar symmetry fall across the horizon, and this hair is classically observable in a memory on the Rindler family of uniformly linearly accelerated observers.…”