The generalized uncertainty principle and the quantum entropy due to spin fields on the Reissner-Nordström black hole background

By using the null tetrad and the ’t Hooft brick-wall model, the quantum entropies of a Reissner-Nordström black hole due to the Weyl neutrino, electromagnetic, massless Rarita-Schwinger and gravitational fields for the source-free case are investigated from a generalized uncertainty principle. The divergence structure for the entropy is demonstrated. In addition to the usual linearly and logarithmically divergent terms, additional quadratic, cubic, biquadratic and other higher order divergences exist near the event horizon in the entropy, which not only depend on the black hole characteristics but also on the spin fields and the gravitational interactions. The terms describe the contribution of the quantum fields to the entropy and the effects of the generalized uncertainty principle on it. If the smallest length scale is taken into account, the contribution of the gravitational interactions to the entropy is found to be a part of the dominant term and very important, and therefore it can not be neglected.