黑洞的量子统计熵

摘要/Abstract

摘要：

避开求解各种粒子波动方程的困难,直接应用量子统计的方法,计算各种坐标描述的黑洞背景下玻色场与费米场的配分函数,得到黑洞熵的积分表达式.然后应用改进的brickwall方法膜模型,计算黑洞的统计熵.在所得结果中取适当的参数,可得到黑洞熵与视界面积成正比的关系,不存在原brickwall方法中的舍去项与对数发散项.整个计算过程,物理图像清楚,计算简单,为研究各种坐标下黑洞熵提供了一条简捷的新途经.

关键词: 量子统计, , 黑洞的统计熵, , 膜模型

Abstract:

Using the method of quantum statistics, the authors derive the partition function of bosonic and fermionic field in various coordinates and obtain the integral expression of the entropy of black hole. Then via the improved brickwallmethod and membrane model, the authors obtain that if they choose proper parameter, the entropyof black hole is proportional to the area of horizon. In their result, the stripped term and the divergent logarithmic term in the original brickwall method no longer exist. The authors offer a new simple and direct way of calculating the entropy of black holes in various coordinates.

Key words: Quantum statistics, Statistical entropy of black hole, Membrane model

中图分类号:

83C57

赵仁, 张丽春. 黑洞的量子统计熵[J]. 数学物理学报, 2004, 4(5): 513-520.

DIAO Ren, ZHANG Li-Chun. Quantum Statistical Entropy of Black Hole[J]. Acta mathematica scientia,Series A, 2004, 4(5): 513-520.

参考文献

［1］Bekenstein J D. Black hole and entropy. Phys Rev, 1973, 7D: 2333
［2］Hawking S W. Paticle greation by black hole. Commun Math Phys, 1975,4: 199
［3］Gibbons G W, Hawking S W. Cosmological event horizon thermodynamics and

particle, creation. Phys Rev, 1977, 15D: 2738
［4］Hochberg D, Kephart T W, York J W. Positivity of entropy in the semic

lassical theory of black hole and radiation. Phys Rev, 1993, 48D: 479
［5］Padmanaban T. Phase volume occupied by a test particle around an incipien

t black hole. Physics letters A, 1989, 136: 203
［6］Lee H, Kim S W, Kim W T. Nonvanishing entropy of extremal charged bl

ack hole. Phys Rev, 1996, 54D: 6559
［7］Gerard't Hooft. On the quantum structure of a black hole. Nucl Phys, 1985, 256: 727
［8］Cognola Gognola, Lecca P. Electromagnetic fields in Schwarzschild and Rei

snerNordstrom geometry: Quantum corrections to the black hole entropy. Phys Rev

, 1998, 57D: 1108
［9］Cai Ronggen G, Ji Jeongyoung, Soh Kwangsup. Action and entropy of black h

ole in spacetiomes with a cosmological constant. Class Quantum Grav, 1998, 15: 2783
［10］Solodukhin S N. Conical singularity and quantum corrections to t

he entropy of a black hole. Phys Rev, 1995, 51D: 609
［11］Lee M H, Kim J K. Entropy of a quantum field in rotating black holes. Phys Rev, 1996, 54D: 3904
［12］Zhao R, Zhang L C, Wu Y Q. Nernst theorem and entropy of the

ReissnerNordstrom black hole. Gen Rel Grav, 2000,32: 1639
［13］Jing J L, Yan M L. Effect of spin on the quantum entropy of black holes

. Phys Rev, 2001, 63D: 084028
［14］Elizabeth Winstanley. Renormalized black hole entropy in antide Sitter

space via the brick wall method. Phys Rev, 2001, 63D
［15］Zhao R, Zhang J F, Zhang L C. Entropy of schwarzschildde Sitter bl

ack hole in nonthermalequilibrium. Modern Physics Letters, 2001, 16A: 719
［16］Zhao R, Zhang J F, Zhang L C. Statistical entropy in ReissnerNords

trom black hole. Nucl Phys, 2001, 602B: 247
［17］Li X, Zhao Z. Entropy of a Vaidya black hole. Phys Rev, 2000, 2D
［18］Tolman R C. Relativity, Thermodynamics and Cosmology. Oxford: Oxford Un

iversity Press, 1934
［19］Gibbons G W, Hawking S W. Action integrals and partition functions in

quantum gravity. Phys Rev, 1977， 15D： 2752
［20］Liu Wenbiao, Zhao Zheng. Entropy of Dirac field in KerrNewman black ho

le. Phys Rev, 2000, 61D
［21］Cai Ronggen, Zhang Yuanzhong. Black planes solutions in fouddimension

al spacetimes. Phys Rev, 1996, 54D: 4891
［22］José P S Lemos, Vilson T, Zanchin. Rotating charged black strings and t

hreedimensional black holes. Phys Rev, 1996， 54D: 3840
［23］Andrew D B. φ\+2 in the spacetime of a cylindrical black hole. Gen Rel Grav, 1999, 31: 1549

[1]	尹建东, 周作领. 熵极小动力系统的复杂性[J]. 数学物理学报, 2015, 35(1): 29-35.
[2]	孙惠, 褚玉明. Toader平均的二次与调和平均界[J]. 数学物理学报, 2015, 35(1): 36-42.
[3]	黄琴, 阮其华. 紧黎曼流形上的椭圆边界值问题[J]. 数学物理学报, 2015, 35(1): 43-49.
[4]	高黎明. 一类含双参量边值问题的多重解[J]. 数学物理学报, 2015, 35(1): 50-55.
[5]	默会霞, 陆善镇. 带变量核的广义高阶Marcinkiewicz积分交换子在Herz型Hardy空间的有界性[J]. 数学物理学报, 2015, 35(1): 56-67.
[6]	肖爽, 蹇明, 陈爱香, 蹇贝. 模糊环境中跳扩散模型下带交易费用的期权定价方法[J]. 数学物理学报, 2015, 35(1): 118-130.
[7]	彭卓华. 矩阵约束下矩阵方程组的双对称最小二乘解[J]. 数学物理学报, 2015, 35(1): 131-150.
[8]	魏美春, 唐春雷. R^N上的Kirchhoff 型问题非平凡解的存在性和多解性[J]. 数学物理学报, 2015, 35(1): 151-162.
[9]	万成高. 随机环境中马氏链函数加权和的极限定理[J]. 数学物理学报, 2015, 35(1): 163-171.
[10]	朴勇杰, 金海兰, 金元峰. TVS -值锥度量空间上四个映射的唯一公共不动点[J]. 数学物理学报, 2015, 35(1): 172-181.
[11]	刘竟成, 李俊锋, 张学军. Cⁿ中单位球上Dirichlet型空间的Cesaro 算子[J]. 数学物理学报, 2015, 35(1): 182-193.
[12]	章春国, 张海燕, 谷尚武. 一类具有局部记忆阻尼的弱耦合系统的能量衰减估计[J]. 数学物理学报, 2015, 35(1): 194-209.
[13]	刘永民, 于燕燕. 关于从混合模空间到小 \|Zygmund 空间的 Volterra 型复合算子[J]. 数学物理学报, 2015, 35(1): 210-217.
[14]	张科, 王珺. 一类复差分方程亚纯解的振荡性质[J]. 数学物理学报, 2015, 35(1): 218-224.
[15]	邵志强. 关于δ初值的Chaplygin 压交通流AR 模型的Riemann问题[J]. 数学物理学报, 2014, 34(6): 1353-1371.