# Horizon symmetries of black holes with supertranslation field

## TL;DR

This paper investigates the near-horizon symmetries of black holes with supertranslation fields, analyzing how these symmetries preserve the metric's structure and calculating associated surface charges.

## Contribution

It characterizes the subgroup of supertranslations preserving the near-horizon structure of black holes with supertranslation fields and examines the integrability of surface charge variations.

## Key findings

- Identified transformations preserving the near-horizon metric structure.
- Calculated surface charges associated with horizon symmetries.
- Discussed conditions for integrability of charge variations.

## Abstract

Near-horizon symmetries are studied for black hole solutions to Einstein equations containing supertranslation field constructed by Compere and Long. The metric is transformed to variables in which the horizon is located at the surface $r=2M$, where $M$ is the mass of black hole. We consider general diffeomorphisms which preserve the gauge and the near-horizon structure of the metric and find the corresponding transformations of metric components. We review the action of the generators of supertranslations preserving the static gauge of the metric and determine a subgroup of supertranslations preserving the gauge and near-horizon structure of the metric. Variation of the surface charge corresponding to the Killing vectors of asymptotic horizon symmetries is calculated. Sufficient conditions of integrability of the variation of the surface charge to a closed integral form are found and an example of metrics with integrable charge variation is discussed.