Near-horizon symmetries of the Schwarzschild black hole with supertranslation field

Abstract

Using the exact solution to Einstein equations of Compere and Long for the Schwarzschild metric containing supertranslation field, we study the near-horizon symmetries of the metric. We consider class of metrics with supertranslation field depending only on a spherical angle $\theta$. After reviewing the action of supertranslations preserving the static gauge of the metric, we study general transformations preserving the near-horizon form of the metric. We determine the asymptotic Killing vectors and calculate the charge corresponding to the asymptotic symmetries preserving the form of the metric at the horizon.

13 pages. Slightly extended published version

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• Symmetries of the Black Hole Interior and Singularity Regularization
• Eikonal quasinormal modes and photon orbits of deformed Schwarzschild black holes
• Near horizon symmetries, emergence of Goldstone modes and thermality
• Can we detect a supertranslated black hole?
• Black Hole Shadow with Soft Hair
• Black holes with supertranslation field, "large transformations" and Israel theorem
• On the Photon Motion Near a Five-Dimensional Schwarzschild Black Hole