Diffeomorphism on Horizon as an Asymptotic Isometry of Schwarzschild Black Hole

TL;DR

This paper proposes a new boundary condition near the Schwarzschild black hole horizon, showing that horizon diffeomorphisms act as asymptotic symmetries, revealing a novel perspective on black hole horizon structure.

Contribution

It introduces a new boundary condition at the horizon allowing horizon diffeomorphisms to be interpreted as asymptotic symmetries, advancing understanding of black hole horizon geometry.

Findings

Horizon diffeomorphisms can be regarded as asymptotic isometries.

A new boundary condition near the horizon admits local time-shift and diffeomorphisms as symmetries.

The approach provides a fresh perspective on the symmetry structure of Schwarzschild black holes.

Abstract

It is argued that the diffeomorphism on the horizontal sphere can be regarded as a nontrivial asymptotic isometry of the Schwarzschild black hole. We propose a new boundary condition of asymptotic metrics near the horizon and show that the condition admits the local time-shift and diffeomorphism on the horizon as the asymptotic symmetry.