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arXiv 1409.2369hep-thgr-qc
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大质量引力下黑洞的热力学

Thermodynamics of Black Holes in Massive Gravity

Rong-Gen Cai, Ya-Peng Hu, Qi-Yuan Pan, Yun-Long Zhang

备注：
Latex 19 pages with 8 figures
发表信息：
Phys. Rev. D 91 (2015) 024032
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摘要：

提出了一类具有负宇宙常数的（$n+2)$）维大质量引力场中的带电黑洞解，并在巨正则系综和正则系综下研究了黑洞解的热力学和相结构.黑洞视界可以具有正的、零的或负的常曲率，其特征在于恒定的$k$。利用Hamilton方法，得到了解的守恒荷，发现黑洞熵仍然服从面积公式，黑洞视界处的引力场方程可以转化为黑洞热力学第一定律形式.在巨正则系综中，我们发现热力学和相结构依赖于四维情况下的组合$k -μ^2/4 +c_2 m^2$，其中$μ$是化学势，$c_2m^2$是与引力子质量相关的势中第二项的系数.当它为正时，黑洞可以发生Hawking-Page相变，而当它为负时，黑洞总是具有正容量的量子稳定的。在正则系综中，四维情况下的组合是$k+c_2m^2$。当它为正值时，如果电荷小于临界电荷，则小黑洞和大黑洞之间可以发生一级相变。在高维（$n+2 \ge 5$）情况下，即使不存在电荷，也可以出现小/大黑洞相变，在大质量引力中与引力子质量相关的势中第三项（$c_3m^2$）和第四项（$c_4m^2$）的系数可以起到与四维情况下电荷相同的作用.

英文摘要：

We present a class of charged black hole solutions in an ($n+2)$-dimensional massive gravity with a negative cosmological constant, and study thermodynamics and phase structure of the black hole solutions both in grand canonical ensemble and canonical ensemble. The black hole horizon can have a positive, zero or negative constant curvature characterized by constant $k$. By using Hamiltonian approach, we obtain conserved charges of the solutions and find black hole entropy still obeys the area formula and the gravitational field equation at the black hole horizon can be cast into the first law form of black hole thermodynamics. In grand canonical ensemble, we find that thermodynamics and phase structure depends on the combination $k -μ^2/4 +c_2 m^2$ in the four dimensional case, where $μ$ is the chemical potential and $c_2m^2$ is the coefficient of the second term in the potential associated with graviton mass. When it is positive, the Hawking-Page phase transition can happen, while as it is negative, the black hole is always thermodynamically stable with a positive capacity. In canonical ensemble, the combination turns out to be $k+c_2m^2$ in the four dimensional case. When it is positive, a first order phase transition can happen between small and large black holes if the charge is less than its critical one. In higher dimensional ($n+2 \ge 5$) case, even when the charge is absent, the small/large black hole phase transition can also appear, the coefficients for the third ($c_3m^2$) and/or the fourth ($c_4m^2$) terms in the potential associated with graviton mass in the massive gravity can play the same role as the charge does in the four dimensional case.

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