环面黑洞的热力学函数

管韵; 王波波

doi:10.7498/aps.70.20212370

摘要

本文把宇宙学常数看成与压强相当的动力学变量, 研究了环面黑洞的热力学函数. 计算得到环面黑洞的状态方程, 环面黑洞的Smarr关系. 然后通过计算其欧氏作用量得到了吉布斯函数, 并进一步求得环面黑洞的自由能、内能和热力学焓, 以及环面黑洞的定压热容和定容热容. 结果表明: 环面黑洞没有范德瓦耳斯型的相变. 环面黑洞的定压热容大于零, 定容热容等于零, 故是一个稳定的热力学系统.

关键词:

The thermodynamic functions of toroidal black holes are investigated in this paper by taking the cosmological constant as a dynamic variable equivalent to the pressure. The equation of state and the Smarr relation of a toroidal black hole are given. Then, the Gibbs function is obtained by calculating the Euclidian action. Further we study other thermodynamic functions of the toroidal black hole, such as free energy, internal energy, and thermodynamic enthalpy. The heat capacity of the toroidal black hole at constant pressure and constant volume is obtained. The results show that toroidal black holes have no van der Waals type phase transition. Toroidal black hole is a stable thermodynamic system because its heat capacity at constant pressure is greater than zero and its heat capacity at constant volume is equal to zero.

Keywords:

作者及机构信息

管韵^1,2,
王波波¹

1.
北京交通大学理学院, 北京　100044

2.
山东大学(威海)空间科学与物理学院, 威海　264209

通信作者: 王波波, bbwang@bjtu.edu.cn

Authors and contacts

Guan Yun^1,2,
Wang Bo-Bo¹

1.
School of Science, Beijing Jiaotong University, Beijing 100044, China

2.
School of Space Science and Physics, Shandong University, Weihai 264209, China

Corresponding author: Wang Bo-Bo, bbwang@bjtu.edu.cn

文章全文

参考文献

[1]	Bekenstein J D 1973 Phys. Rev. D 7 2333 Google Scholar
[2]	Bekenstein J D 1974 Phys. Rev. D 9 3292 Google Scholar
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[11]	Gibbons G W, Hawking S W 1977 Phys. Rev. D 15 2752 Google Scholar
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施引文献

图 1 环面黑洞的等温图

Fig. 1. Isotherm of toroidal black hole.

下载: 全尺寸图片幻灯片

图 2 环面黑洞吉布斯函数

Fig. 2. Gibbs function of toroidal black hole.

下载: 全尺寸图片幻灯片

[1]	Bekenstein J D 1973 Phys. Rev. D 7 2333 Google Scholar
[2]	Bekenstein J D 1974 Phys. Rev. D 9 3292 Google Scholar
[3]	Hawking S W 1975 Commun. Math. Phys. 43 199 Google Scholar
[4]	Caldarelli M M, Cognola G, Klemm D 2000 Class. Quantum Grav. 17 399 Google Scholar
[5]	Kastor D, Ray S, Traschen J 2009 Class. Quantum Grav. 26 195011 Google Scholar
[6]	Dolan B P 2011 Class. Quantum Grav. 28 125020 Google Scholar
[7]	Dolan B P 2011 Class. Quantum Grav. 28 235017 Google Scholar
[8]	Dolan B P 2011 Phys. Rev. D 84 127503 Google Scholar
[9]	Cvetic M, Gibbons G W, Kubizňák D, Pope C N 2011 Phys. Rev. D 84 024037 Google Scholar
[10]	Lu H, Pang Y, Pope C N, et al. 2012 Phys. Rev. D 86 044011 Google Scholar
[11]	Gibbons G W, Hawking S W 1977 Phys. Rev. D 15 2752 Google Scholar
[12]	Kubizňák D, Mann R B 2012 JHEP 7 1 Google Scholar
[13]	Wang B B 2004 Gen. Relat. Gravit. 36 735 Google Scholar
[14]	Wang B B 2008 Chin. Phys. B 17 467 Google Scholar
[15]	Goenner H, Stachel J 1970 J. Math. Phys. 11 3358 Google Scholar
[16]	Huang C G, Liang C B 1995 Phys. Lett. A 201 27 Google Scholar
[17]	梁灿彬, 周彬 2009 微分几何入门与广义相对论(下册) 第二版 (北京: 科学出版社) 第116页 Liang C B, Zhou B 2009 Introduction to Differential Geometry and General Relativity (Vol. 2) (2nd Ed.) (Beijing: Science Press) p116 (in Chinese)
[18]	Gauntlett J P, Myers R C, Townsend P K 1999 Class. Quant. Grav. 16 1 Google Scholar
[19]	Townsend P. K. and Zamaklar M. 2001 Class. Quant. Grav. 18 5269 Google Scholar

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