ONE-LOOP QUANTUM CORRECTIONS TO THE ENTROPY FOR A 4-DIMENSIONAL ETERNAL BLACK-HOLE

The first quantum corrections to the free energy for an eternal four-dimensional black hole are investigated at one-loop level, in the large mass limit of the black hole, making use of the conformal techniques related to the optical metric. The quadratic and logarithmic divergences as well as a finite part associated with the first quantum correction to the entropy are obtained at a generic temperature. It is argued that, at the Hawking temperature, the horizon divergences of the internal energy should cancel. Some comments on the divergences of the entropy are also presented.