Diffeomorphism on Horizon as an Asymptotic Isometry of Schwarzschild Black Hole

TL;DR

The paper investigates whether diffeomorphisms on the Schwarzschild horizon can be treated as nontrivial asymptotic isometries by introducing general near-horizon boundary conditions. It identifies a symmetry algebra consisting of a local horizon time shift and sphere diffeomorphisms, and computes finite horizontal charges via the ADM/Noether formalism, demonstrating a nontrivial, non-singlet representation without a central extension. This horizon symmetry provides a classical arena for black hole hair-like degrees of freedom, with potential relevance to entropy counting, though it does not yield a central charge suitable for Cardy-like microstate enumeration. Overall, the work argues that horizon diffeomorphisms are physical and may contribute to the holographic structure of 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.