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

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.