Remarks on Renormalization of Black Hole Entropy

We elaborate the renormalization process of entropy of a nonextremal and an extremal Reissner-Nordstr"{o}m black hole by using the Pauli-Villars regularization method, in which the regulator fields obey either the Bose-Einstein or Fermi-Dirac distribution depending on their spin-statistics. The black hole entropy involves only two renormalization constants. We also discuss the entropy and temperature of the extremal black hole.