Diffeomorphism on Horizon as an Asymptotic Isometry of Schwarzschild   Black Hole
  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. 
M. Hotta, K. Sasaki, T. Sasaki