Thermodynamic features of black holes dressed with quantum fields

The thermal properties of black holes in the presence of quantum fields can be revealed through solutions of the semi-classical Einstein equation. We present a brief but self-contained review of the main features of the semi-classical back reaction problem for a black hole in the microcanonical ensemble. The solutions, obtained for conformal scalars, massless spinors and U(1) gauge bosons, are used to calculate the O(\hbar) corrections to the temperature and thermodynamical entropy of a Schwarzschild black hole. In each spin case considered, the entropy corrections \Delta S(r), are positive definite and monotone increasing with increasing distance r from the hole, and are of the same order as the naive flat space radiation entropy