Reissner-Nordstr\"{o}m black holes statistical ensembles and first order   thermodynamic phase transition
  We apply Debbasch proposal to obtain mean metric of coarse graining (statistical ensemble) of quantum perturbed Reissner-Nordst\"{o}m black hole $(RNBH).$ Then we seek its thermodynamic phase transition behavior. Our calculations predict first order phase transition which it can take Bose Einstein's condensation behavior. 
Hossein Ghaffarnejad and Mohammad Farsam
physics.gen-ph