Horizon supertranslation and degenerate black hole solutions

TL;DR

This paper reviews degenerate vacua from BMS symmetries and derives infinitely degenerate black hole solutions related by horizon supertranslations, extending the understanding of near-horizon symmetries and solutions.

Contribution

It introduces a framework for defining BMS-like supertranslations at black hole horizons and derives new degenerate solutions in near-horizon approximations.

Findings

Derivation of infinitely degenerate black hole solutions

Relation of solutions via horizon supertranslations

Extension to higher order and Rindler horizons

Abstract

In this note we first review the degenerate vacua arising from the BMS symmetries. According to the discussion in [1] one can define BMS-analogous supertranslation and superrotation for spacetime with black hole in Gaussian null coordinates. In the leading and subleading orders of near horizon approximation, the infinitely degenerate black hole solutions are derived by considering Einstein equations with or without cosmological constant, and they are related to each other by the diffeomorphism generated by horizon supertranslation. Higher order results and degenerate Rindler horizon solutions also are given in appendices.