# Large gravitons and near-horizon diffeomorphisms

## TL;DR

This paper explores the connection between asymptotic symmetries at infinity and near-horizon regions of black holes, using wave equations to relate these symmetries in the context of BTZ and Kerr black holes.

## Contribution

It introduces a novel method linking horizon and infinity symmetries via wave equations, applied to BTZ and Kerr black holes, revealing a circle diffeomorphism group.

## Key findings

- Realization of the diffeomorphism group of the circle at horizons
- Method applicable to both BTZ and Kerr black holes
- Proposes a new approach to relate asymptotic symmetries

## Abstract

Usual gauge fixing procedures in classical general relativity rely on the existence of solutions of a second order wave equation. We propose to use the equation to relate asymptotic symmetries at infinity to asymptotic symmetries of a black hole horizon, in tune with recent proposals. We illustrate the construction for the BTZ and four-dimensional Kerr black holes. We find in both cases a realization of the group of diffeomorphisms of the circle $S^1$.