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

TL;DR

This paper investigates the near-horizon symmetries of a Schwarzschild black hole with supertranslation fields, identifying asymptotic Killing vectors and associated charges, thus extending understanding of horizon symmetries in modified black hole solutions.

Contribution

It provides a detailed analysis of near-horizon symmetries for Schwarzschild black holes with supertranslation fields, including explicit calculations of asymptotic Killing vectors and charges.

Findings

Identified the class of near-horizon symmetries preserving the metric form.

Calculated the charges associated with these asymptotic symmetries.

Extended the understanding of horizon symmetries in black holes with supertranslation fields.

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.