No contributions to the extremal–black-hole entropy from spin fields

The entropy of the extremal Reissner-Nordström black hole due to the gravitational, electromagnetic, neutrino and scalar fields is investigated by using the brick-wall model. Whether extremalization or quantization are carried out first, the entropy satisfies the Nernst theorem when the inner Cauchy horizon is taken into account. Therefore the quantum entropy of the extremal black hole, calculated via the brick-wall model, does not require any regularization