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

• Published in: Physical review. D 2021-08, Vol.104 (4), p.1, Article 044050
• Main Author: Iofa, Mikhail Z.
• Format: Article
• Language: English
• Subjects: Black holes; Coordinates; Einstein equations; Fields (mathematics); Horizon; Isomorphism; Mathematical analysis; Surface charge; Transformations
• ISSN: 2470-0010; 2470-0029
• DOI: 10.1103/PhysRevD.104.044050

Near-horizon symmetries are studied for static black hole solutions to Einstein equations containing a supertranslation field. A supertranslation field is defined at the unit sphere. 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 horizon symmetries of the metric are calculated in different coordinate systems connected by "large" transformations containing a supertranslation field in the metric. Variations of the surface charge corresponding to horizon symmetries are calculated in different coordinate systems. It is shown that the variations of the charge in systems connected by a large transformation have different integrability properties over the space of metrics. In the case of a supertranslation field depending only on the spherical angle θ it is shown that, although the variations of the surface charge in two coordinate systems connected by a large transformation are equal to each other, in one coordinate system the charge variation, having the form of variation of a functional of metrics, is integrable, but in another system it is not.