Diffeomorphism symmetries near a timelike surface in black hole spacetime

TL;DR

This paper investigates the symmetries near a timelike surface at arbitrary radius in Schwarzschild and Kerr black hole spacetimes, revealing a BMS-like algebra that may shed light on horizon degrees of freedom and thermodynamics.

Contribution

It extends the analysis of gravitational symmetries to timelike surfaces inside black hole spacetimes, uncovering a BMS-like algebra at arbitrary radial positions.

Findings

Symmetry algebra resembles BMS symmetry found at null infinity.

The analysis applies to both Schwarzschild and Kerr black holes.

Symmetries are identified on timelike hypersurfaces outside the horizon.

Abstract

Recently symmetries of gravity and gauge fields in the asymptotic regions of spacetime have been shown to play vital role in their low energy scattering phenomena. Further, for the black hole spacetime, near horizon symmetry has been observed to play possible role in understanding the underlying degrees of freedom for thermodynamic behaviour of horizon. Following the similar idea, in this paper, we analyzed the symmetry and associated algebra near a timelike surface which is situated at any arbitrary radial position and is embedded in black hole spacetime. In this paper we considered both Schwarzschild and Kerr black hole spacetimes. The families of hypersurfaces with constant radial coordinate (outside the horizon) in these spacetimes is timelike in nature and divide the space into two distinct regions. The symmetry algebra turned out to be reminiscent of Bondi-Metzner-Sach (BMS) symmetry, found in the asymptotic null infinity.