Black hole fluctuations and dynamics from back-reaction of Hawking   radiation: Current work and further studies based on stochastic gravity
  We give a progress report of our research on spacetime fluctuations induced by quantum fields in an evaporating black hole and a black hole in quasi-equilibrium with its Hawking radiation. We note the main issues involved in these two classes of problems and outline the key steps for a systematic quantitative investigation. This report contains unpublished new ideas for further studies. 
B. L. Hu, Albert Roura