Black hole thermodynamics: No inconsistency via the inclusion of the missing $P-V$ terms
Black hole thermodynamics: No inconsistency via the inclusion of the missing $P-V$ terms
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DOI：
10.1103/physrevd.91.064049
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发表时间：
2014-11
影响因子：
5
通讯作者：
M. Azreg-Ainou
中科院分区：
文献类型：
--
作者：
M. Azreg-Ainou
早期关于黑洞热力学的文献忽略了与黑洞解中存在的基本物理常数相关的P - V项。在第一定律中包含这个常数与Smarr关系不一致。一旦引入了缺失的P - V项，通常只在存在负宇宙学常数的问题中引入它。这种做法继承自宇宙学方法，认为量- Λ / 8 π是由于宇宙流体造成的恒定压力。然而，黑洞热力学中的压强和热力学体积的概念与经典热力学中的压强和热力学体积的概念有很大的不同。从这个角度来看，没有先验的令人信服的理由不扩展压力的概念，并将分压与每个“外部”密度8 π T T T联系起来。在这项工作中，我们将分压与可变质量参数以及有效应力-能量张量t ^ f μ ν的每个t ^ t分量联系起来，但不与电磁场的线性分量联系起来。利用场方程G μ ν = 8 π T eff μ ν，导出了静态（非旋转）带电黑洞的焓、内能、自由能、热力学体积、状态方程、对应态定律、临界性和临界指数的通用表达式，无论它们是否为爱因斯坦场方程的解，它们都可能具有可变的质量参数。我们将推导推广到黑洞沉浸在精质力场中的情况和多力情况。考虑了许多应用和扩展，包括在以前和现在的工作中导出的正则黑洞的应用。在它们的热力学中没有发现不一致。
The early literature on black hole thermodynamics ignored the P - V term associated with the existence of a fundamental physical constant in the black hole solution. The inclusion of this constant in the first law becomes inconsistent with the Smarr relation. Once the missing P - V term is introduced, it becomes customary to introduce it only in problems where there is a negative cosmological constant. This practice is inherited from cosmological approaches which consider the quantity - Λ / 8 π as the constant pressure due to a cosmological fluid. However, the notions of pressure and thermodynamic volume in black hole thermodynamics are very different from their counterparts in classical thermodynamics. From this point of view, there is a priori no compelling reason to not extend this notion of pressure and associate a partial pressure with each “external” density 8 π T t t . In this work, we associate a partial pressure with a variable mass parameter as well as with each t t component of the effective stress-energy tensor T eff μ ν but not with the linear component of the electromagnetic field. Using the field equations G μ ν = 8 π T eff μ ν , we derive universal expressions for the enthalpy, internal energy, free energies, thermodynamic volume, equation of state, law of corresponding states, criticality, and critical exponents of static (nonrotating) charged black holes, with possibly a variable mass parameter, whether they are solutions to the Einstein field equations or not. We extend the derivation to the case where the black hole is immersed in the field of a quintessence force and to the multiforce case. Many applications and extensions are considered, including applications to regular black holes derived in previous and present work. No inconsistency has been noticed in their thermodynamics.