Large gravitons and near-horizon diffeomorphisms

Usual gauge fixing procedures in classical general relativity rely on the existence of solutions of a second order wave equation. We propose to use these equations 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 Banados-Teitelboim-Zanelli (BTZ) and four-dimensional Kerr black holes. We find in both cases a realization of the group of diffeomorphisms of the real line.