One-loop quantum corrections to the entropy for an extremal Reissner-Nordström black hole

The first quantum corrections to the entropy for an eternal four-dimensional extremal Reissner-Nordstr\"om black hole is investigated at the one-loop level, in the large mass limit of the black hole, making use of the conformal techniques related to the optical metric. A leading exponential 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.