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

The total quantum statistical entropy of Reissner-Nordstromblack 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>r_o), region 2 ( r_o > r > r_i), andregion 3 (r_i >r>0), where r_o is theradius of the outer event horizon, and r_i is the radius of theinner event horizon. The total quantum statistical entropy ofReissner-Nordstrom black holes is S=S₁+S₂+S₃, where S_i (i=1,2,3) is the entropy, contributed by regions1,2,3. The detailed calculation shows that S₂ is neglectfullysmall. S₁=w_t(π²/45)k_b(A_o/ε²β³), S₃=-w_t(π²/45)k_b(A_i/ε²β³),where A_o and A_i are, respectively, the areas of theouter and inner event horizons, w_t=2^s[1-2^-(s+1)],s=d/2, d is the space-time dimension, here d=4, s=2. Asr_i approaches r_o in the extreme case the totalquantum statistical entropy of Reissner-Nordstrom black holes approaches zero.