Effects of the generalized uncertainty relation on the quantum entropy of the Schwarzschild black hole due to spin fields

Abstract

By using the brick-wall model, the quantum entropies of the Schwarzschild 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 relation. It is shown that in addition to the usual quadratically and logarithmically divergent terms, there exist additional quadratic, biquadratic and logarithmic divergences, which not only depend on the black hole characteristics but also on the spins of the fields and the gravity correction factor. These additional terms describe the contribution of the quantum fields to the entropy and the effect of gravitational interactions on it. We then take the smallest length scale into account and find that the contribution of the gravitational interactions to the entropy becomes a part of the dominant term and very important so that it cannot be neglected.