Quantum gravity effect on the entropy of a novel four-dimensional Gauss-Bonnet black hole

Abstract

Taking the generalized uncertainty principle into account, we apply the corrected state density and brick-wall method to calculate the entropy of a novel four-dimensional Gauss-Bonnet black hole surrounded by an arbitrary field with spin . It is shown that the leading and logarithmic terms of the entropy are respectively modified by the quantum gravity effect and spin of the field. Meanwhile, the correction coming from gravitational interaction has the same form as the leading term, that is, they all are proportional to the horizon area and inversely proportional to the gravity correction factor. The ratio of the correction term to the leading one is respectively −5/7 and −1395/1764 for Bose and Fermi cases, where negative sign means that the effect of quantum gravity decreases the entropy. It is very interesting that these proportion values are independent of the black hole characteristics.