The total quantum statistical entropy of Reissner-Nordstrom black holes inDirac field case is evaluated in this article. The space-time of the black holes is divided intothree regions: region 1 (r 】 r_o), region 2 (r...The total quantum statistical entropy of Reissner-Nordstrom black holes inDirac field case is evaluated in this article. The space-time of the black holes is divided intothree regions: region 1 (r 】 r_o), region 2 (r_o 】 r 】 r_i), and region 3 (r_i 】 r 】 0), where r_ois the radius of the outer event horizon, and Ti is the radius of the inner event horizon. The totalquantum statistical entropy of Reissner-Nordstrom black holes is S = S_1 + S_2 + S_3, where S_i (i= 1,2,3) is the entropy, contributed by regions 1,2,3. The detailed calculation shows that S_2 isneglectfully small. S_1 = w_t(π~2/45)k_b(A_o/ε~2β~3), S_3 = -w_t(π~2/45)k_b(A_i/ε~2β~3), whereA_o and A_i are, respectively, the areas of the outer 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. As r_i approaches r_o in theextreme case the total quantum statistical entropy of Reissner-Nordstrom black holes approacheszero.展开更多
Using the Unruh-Verlinde temperature obtained by the idea of entropy force,we directly calculated the partition functions of Boson field in Reissner-Nordstro¨m spacetime with quantum statistical method.We obtain ...Using the Unruh-Verlinde temperature obtained by the idea of entropy force,we directly calculated the partition functions of Boson field in Reissner-Nordstro¨m spacetime with quantum statistical method.We obtain the expression of the black hole quantum statistical entropy.We find that the term is proportional to the area of black hole horizon and the logarithmic correction term appears.Our result is valid for flat spacetime.展开更多
文摘The total quantum statistical entropy of Reissner-Nordstrom black holes inDirac field case is evaluated in this article. The space-time of the black holes is divided intothree regions: region 1 (r 】 r_o), region 2 (r_o 】 r 】 r_i), and region 3 (r_i 】 r 】 0), where r_ois the radius of the outer event horizon, and Ti is the radius of the inner event horizon. The totalquantum statistical entropy of Reissner-Nordstrom black holes is S = S_1 + S_2 + S_3, where S_i (i= 1,2,3) is the entropy, contributed by regions 1,2,3. The detailed calculation shows that S_2 isneglectfully small. S_1 = w_t(π~2/45)k_b(A_o/ε~2β~3), S_3 = -w_t(π~2/45)k_b(A_i/ε~2β~3), whereA_o and A_i are, respectively, the areas of the outer 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. As r_i approaches r_o in theextreme case the total quantum statistical entropy of Reissner-Nordstrom black holes approacheszero.
基金supported by the National Natural Science Foundation of China (Grant Nos.11175109 and 11075098)the Shanxi Datong University Doctoral Sustentation Fund (Grant Nos.2008-B-06,2011-B-04 and 2008Q8)
文摘Using the Unruh-Verlinde temperature obtained by the idea of entropy force,we directly calculated the partition functions of Boson field in Reissner-Nordstro¨m spacetime with quantum statistical method.We obtain the expression of the black hole quantum statistical entropy.We find that the term is proportional to the area of black hole horizon and the logarithmic correction term appears.Our result is valid for flat spacetime.
