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

The total quantum statistical entropy of Reissner-Nordstrom black holes in Dirac field case is evaluated in this article. The space-time 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 Reissner-Nordstrom black holes is S = S1+S2+S3, where Si (i = 1,2,3) is the entropy, contributed by regions 1,2,3. The detailed calculation shows that S2 is neglectfully small. S1 = wt(π2/45)kb(Ao/ε2β3), S3 = -wt(π2/45)kb(Ai/ε2β3), where Ao and Ai are, respectively, the areas of the outer and inner event horizons, wt = 2s[1-2-(s+1)], s = d/2, d is the space-time dimension, here d = 4, s = 2. As ri approaches ro in the extreme case the total quantum statistical entropy of Reissner-Nordstrom black holes approaches zero.