Symmetries at the black hole horizon

Abstract

We determine the asymptotic symmetry group of Killing horizons by choosing Gaussian null coordinates in the neighbourhood of the horizon and boundary conditions that respect the leading order terms in the metric. The analysis divides naturally into the two cases of subextremal and extremal horizons. In general, we find rather involved asymptotic symmetry generators that nevertheless involve supertranslations and Killing vectors on the compact horizon. The most striking observation is the difference in the dependence on the coordinate along the horizon; we relate this to the redshift effect for subextremal horizons. We consider the spherically symmetric case as a special and illuminating example.

arXiv comment18 pages

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• BMS Goldstone modes near the horizon of a Kerr black hole are thermal
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• Corrections to the Aretakis type behaviour of the metric due to an infalling particle
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• All near-horizon symmetries of the Schwarzschild black hole in linearised gravity
• Supersymmetric near-horizon geometries in D = 6 supergravity: Lichnerowicz theorems, index theory and symmetry enhancement