Renyi entropies of a black hole from Hawking radiation
  Renyi entropies of a black hole are evaluated by counting the states of the Hawking radiation which fills a thin shell surrounding the horizon. The width of the shell is determined from its energy content and the corresponding mass defect. The Bekenstein-Hawking formula for the entropy of the black hole is correctly reproduced. 
A.Bialas and W.Czyz