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arXiv 1607.05445hep-th
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反德西特和德西特时空的修正热力学第一热力学定律

The modified first laws of thermodynamics of anti-de Sitter and de Sitter space-times

Deyou Chen, Qingyu Gan, Jun Tao

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20 pages,6 figures, minor corrections
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摘要：

利用表面张力修正了Reissner-Nordstrom反de Sitter黑洞和纯de Sitter时空的热力学第一热力学定律.服从相应的Smarr关系。首先将宇宙学常数视为固定常数，然后将其视为与压力相关的变量。对于黑洞，当宇宙学常数固定时，定律写为$δE = T δS - σδA$，其中$E$是Misner-Sharp质量，$σ$是表面张力。采用变常数的方法，将该定律修正为$δE_0 = T δS - σ_{eff}δA +VδP$，其中$E_0=M-\frac{Q^2}{2r_+}$为焓。研究了其结晶性能。对于de Sitter时空，修正定律的表达式与黑洞的不同。讨论了推导该定律的微分方法。

英文摘要：

We modify the first laws of thermodynamics of a Reissner-Nordstrom anti-de Sitter black hole and a pure de Sitter space-time by the surface tensions. The corresponding Smarr relations are obeyed. The cosmological constants are first treated as fixed constants, and then as variables associated to the pressures. For the black hole, the law is written as $δE = T δS - σδA$ when the cosmological constant is fixed, where $E$ is the Misner-Sharp mass and $σ$ is the surface tension. Adopting the varied constant, we modify the law as $δE_0 = T δS - σ_{eff}δA +VδP$, where $E_0=M-\frac{Q^2}{2r_+}$ is the enthalpy. The thermodynamical properties are investigated. For the de Sitter space-time, the expressions of the modified laws are different from these of the black hole. The differential way to derive the law is discussed.

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