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Total Quantum Statistical Entropy of Reissner-Nordstrom Black Holes: Scalar Field Case

The total quantum statistical entropy of Reissner-Nordstrom (RN) black holes is evaluated. The spacetime of the black holes is divided into three regions - region 1, (r > ro); region 2, (ro > r > ri); and region 3, (ri > r > 0) - where ro is the radius of the outer event horizon, and ri is the radius of the inner event horizon. The total quantum statistical entropy of RN black holes is S = S1 + S2 + S3, where Si (i = 1,2,3) is the entropy, contributed by region Si (i = 1,2,3). The detailed calculation shows that S2≈0. S1 = (π2/45)[kbAo/ϵ2β3], S3 = -(π2/45)[kbAi/ϵ2β3], where Ao and Ai are, respectively, the area of the outer and inner event horizons. Thus, as ri approaches ro, in the extreme case the total quantum statistical entropy of RN black holes approaches zero.