Quantum Statistical Entropy of Five-Dimensional BlackHole

Abstract

The generalized uncertainty relation is introduced to calculatequantum statistic entropy of a black hole. By using thenew equation of state density motivated by the generalizeduncertainty relation, we discuss entropies of Bose field and Fermifield on the background of the five-dimensional spacetime. In ourcalculation, we need not introduce cutoff. There is not thedivergent logarithmic term as in the original brick-wall method. Andit is obtained that the quantum statistic entropy corresponding toblack hole horizon is proportional to the area of the horizon.Further it is shown that the entropy of black hole is the entropy ofquantum state on the surface of horizon. The black hole's entropyis the intrinsic property of the black hole. The entropy is aquantum effect. It makes people further understand the quantum statistic entropy.