Black Hole Horizon Fluctuations
  It is generally admitted that gravitational interactions become large at an invariant distance of order $1$ from the black hole horizon. We show that due to the ``atmosphere'' of high angular particles near the horizon strong gravitational interactions already occur at an invariant distance of the order of $\sqrt[3]{M}$. The implications of these results for the origin of black hole radiation, the meaning of black hole entropy and the information puzzle are discussed. 
A.Casher, F. Englert, N.Itzhaki, S.Massar, R. Parentani