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

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 near-horizon structure of metric. Diffeomorphisms generated by vector fields form a group symmetries. The densities variation surface charge associated asymptotic horizon metric calculated in different coordinate systems connected "large" transformations change field Integrability variations surfacecharge is considered systems. case integrable detail.