Quantum Statistical Entropy of Non-extreme and Nearly ExtremeBlack Holes in Higher-Dimensional Space-Time

Abstract

The free energy and entropy of Reissner-Nordstrom black holes inhigher-dimensional space-time are calculated by the quantum statistic methodwith a brick wall model. The space-time of the black holes is dividedinto three regions: region 1, (r > ro); region 2, (ro > r > ri);and region 3, (ri > r > 0), where ro is the radius of the outerevent horizon, and ri is the radius of the inner event horizon.Detailed calculation shows that the entropy contributed by region 2is zero, the entropy contributed by region 1 is positive andproportional to the outer event horizon area, the entropy contributed byregion 3 is negative and proportional to the inner event horizon area.The total entropy contributed by all the three regions is positive andproportional to the area difference between the outer and innerevent horizons. As ri approaches ro in the nearly extremecase, the total quantum statistical entropy approaches zero.