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-d imensional 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 divergenc es as well as a finite part associated with the first quantum correcti on to the entropy are obtained at a generic temperature. It is argued that, at the Hawking temperature, the horizon divergences of the inter nal energy should cancel. Some comments on the divergences of the entr opy are also presented.