ONE-LOOP QUANTUM CORRECTIONS TO THE ENTROPY FOR AN EXTREMAL REISSNER-NORDSTROM BLACK-HOLE

The first quantum corrections to the entropy for an eternal four-dimen sional extremal Reissner-Nordstrom black hole is investigated at the o ne-loop level, in the large mass limit of the black hole, making use o f the conformal techniques related to the optical metric. A leading ex ponential horizon divergence is found and other divergences appear due to the singular nature of the optical manifold. The area law is shown to be violated.