All near-horizon symmetries of the Schwarzschild black hole in linearised gravity

TL;DR

This paper identifies all potential near-horizon symmetries of the Schwarzschild black hole in linearised gravity, revealing a large set of physical symmetries, including two copies of u(1) for large black holes, which could influence gravitational scattering and black hole evaporation.

Contribution

It systematically finds the most general near-horizon symmetries in linearised gravity without boundary conditions, expanding understanding of horizon symmetries relevant to gravitational processes.

Findings

Most general near-horizon symmetries are identified.

Associated charges are finite and non-zero, confirming physical relevance.

For large black holes, dominant symmetries are two copies of u(1).

Abstract

Asymptotic symmetries are known to constrain the infrared behaviour of scattering processes in asymptotically flat spacetimes. By the same token, one expects symmetries of the black hole horizon to constrain near-horizon gravitational scattering. In this paper, we take a step towards establishing this connection. We find all near-horizon symmetries that can be potentially relevant to gravitational scattering near the horizon of the Schwarzschild black hole. We study large diffeomorphisms of linearised perturbations of the Schwarzschild black hole in a partial wave basis and in a gauge that allows for gravitational radiation crossing the event horizon. This setup is ideally suited for studying processes involving near-horizon gravitons like scattering and black hole evaporation. We find the most general near-horizon symmetries that are consistent with finite perturbations at the horizon. Since we do not impose any further boundary conditions, these symmetries represent the biggest set of symmetries in this setting. We find the associated covariant charges to be finite and non-zero showing that these symmetries are physical. Interestingly, for a large black hole, the dominant symmetries are just two copies of $ u(1)$.