Stability and fluctuations in black hole thermodynamics
Stability and fluctuations in black hole thermodynamics
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DOI：
10.1103/physrevd.75.024037
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发表时间：
2007-01
影响因子：
5
通讯作者：
George Ruppeiner
中科院分区：
文献类型：
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作者：
George Ruppeiner
我研究热力学波动的Kerr-Newman黑洞在一个广泛的，无限的环境。这个问题并不是严格可解的，因为任何质量为M、角动量为J、电荷为Q的黑洞都无法在这样的环境中达到完全平衡。然而，如果我们认为M、J或Q中的一个（或两个）相对于其他的变化如此缓慢，我们可以认为它是固定的，稳定的例子就会出现，热力学涨落理论就可以合理地应用。我研究了七个案例，其中有一个，两个或三个独立的波动变量。不需要关于环境的热力学行为的知识。黑洞的热力学是足够的。设热力学量X的涨落矩为{radical}（）。在固定M的波动是稳定的所有热力学状态，包括非旋转和不带电的环境，对应于平均值J=Q=0。这里，J和Q的波动矩取最大值。J与M成正比。对于普朗克质量，它是0.3990（{Dirac_h}/2{pi}）。Q = 3.301e，与M无关。在所有情况下，M、J和Q的涨落矩在物理状态的极限处趋于零，在那里温度趋于零。随着M的波动，没有平均J=Q=0的稳定情况。但是，有过渡到稳定的标志是无限波动。对于纯粹的M波动，这与戴维斯确定为相变的曲线相吻合。«少
I examine thermodynamic fluctuations for a Kerr-Newman black hole in an extensive, infinite environment. This problem is not strictly solvable because full equilibrium with such an environment cannot be achieved by any black hole with mass M, angular momentum J, and charge Q. However, if we consider one (or two) of M, J, or Q to vary so slowly compared with the others that we can regard it as fixed, instances of stability occur, and thermodynamic fluctuation theory could plausibly apply. I examine seven cases with one, two, or three independent fluctuating variables. No knowledge about the thermodynamic behavior of the environment is needed. The thermodynamics of the black hole is sufficient. Let the fluctuation moment for a thermodynamic quantity X be {radical}( ). Fluctuations at fixed M are stable for all thermodynamic states, including that of a nonrotating and uncharged environment, corresponding to average values J=Q=0. Here, the fluctuation moments for J and Q take on maximum values. That for J is proportional to M. For the Planck mass it is 0.3990({Dirac_h}/2{pi}). That for Q is 3.301e, independent of M. In all cases, fluctuation moments for M, J, and Q go to zero at the limit of the physicalmore » regime, where the temperature goes to zero. With M fluctuating there are no stable cases for average J=Q=0. But, there are transitions to stability marked by infinite fluctuations. For purely M fluctuations, this coincides with a curve which Davies identified as a phase transition.« less