Surface charge of horizon symmetries of a black hole with supertranslation field

TL;DR

This paper investigates the near-horizon symmetries of static black holes with supertranslation fields, focusing on surface charge variations and their integrability across different coordinate systems.

Contribution

It analyzes the structure of horizon symmetries and surface charge variations in black holes with supertranslation fields, including the effects of large transformations.

Findings

Surface charge densities are computed for various coordinate systems.

The integrability of surface charge variations is examined in detail.

Large transformations affect the supertranslation field and the associated charges.

Abstract

Near-horizon symmetries are studied for static black hole solutions to Einstein equations containing supertranslation field. We consider general diffeomorphisms which preserve the gauge and the near-horizon structure of the metric. Diffeomorphisms are generated by the vector fields and form a group of near-horizon symmetries. The densities of variation of the surface charge associated to asymptotic horizon symmetries of the metric are calculated in different coordinate systems connected by "large" transformations which change supertranslation field in the metric. Integrability of the variations of surfacecharge is considered in different coordinate systems. The case of integrable variation of the surface charge is studied in detail.