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arXiv 2407.00484gr-qcastro-ph.COhep-th
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广义熵意味着变化的G：依赖视界面积的场方程与黑洞-宇宙学耦合

Generalized Entropy Implies Varying-G: Horizon Area Dependent Field Equations and Black Hole-Cosmology Coupling

Hengxin Lu, Sofia Di Gennaro, Yen Chin Ong

备注：
Minor changes; also added/fixed some references; published version
发表信息：
Annals of Phys. 474 (2025) 169914
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AI总结：

该研究基于雅各布森热力学推导引力方程的方法，指出广义熵会导致依赖视界面积的变化有效引力常数，证明量子引力对数修正等价于跑动引力常数，并揭示黑洞-宇宙学耦合的理论动机，简化了Tsallis熵下史瓦西黑洞的热力学质量计算。

摘要：

当贝肯斯坦-霍金熵被修正时，关于霍金温度还是热力学质量应被修正的问题常常会出现歧义。然而，常见的做法是保持黑洞解与广义相对论中的解相同。另一方面，如果雅各布森从热力学推导爱因斯坦方程的方法在一般情形下成立，那么给定一个广义熵，人们应该首先推导出相应的修正引力理论，然后寻找相容的黑洞解，之后再研究其热力学性质。我们评述了这种方法中的一些性质和微妙之处。特别地，我们指出，广义熵通常会导致一种有效引力“常数”变化的理论，其中$G_\ ext{eff}$依赖于视界面积。我们讨论了尽管这类理论看似存在显著差异，但仍能通过哪些方式与广义相对论区分开来，以及如何理解依赖面积的场方程。作为结果，我们证明在雅各布森方法中，对贝肯斯坦-霍金熵的标准量子引力对数修正等价于一个跑动的引力“常数”。依赖视界面积的$G_\ ext{eff}$还可能导致黑洞质量与宇宙膨胀之间的耦合，这一情景最近在文献中已有研究，但迄今为止缺乏强有力的理论动机。在Tsallis熵的情形下，我们证明史瓦西黑洞的热力学质量恰好是其ADM质量的一个常数倍，这比不采用雅各布森方法的处理方式要简单得多。

英文摘要：

When the Bekenstein-Hawking entropy is modified, ambiguity often arises concerning whether the Hawking temperature or the thermodynamic mass should be modified. The common practice, however, is to keep the black hole solution the same as that in general relativity. On the other hand, if Jacobson's method of deriving Einstein equations from thermodynamic is valid in the general settings, then given a generalized entropy one should first derive the corresponding modified gravity, and then look for the compatible black hole solution before investigating its thermodynamics. We comment on some properties and subtleties in this approach. In particular, we point out that generically generalized entropy would lead to a varying effective gravitational "constant" theory, where $G_\text{eff}$ depends on the horizon area. We discuss in what ways such theories are discernible from general relativity despite its seemingly jarring differences, and how to make sense of area-dependent field equations. As a consequence we show that in the Jacobson's approach, the standard quantum gravitational logarithmic correction to Bekenstein-Hawking entropy is equivalent to a running gravitational "constant". A horizon area dependent $G_\text{eff}$ could also lead to a coupling between black hole masses and cosmological expansion, a scenario that has been studied recently in the literature, but so far lacks strong theoretical motivation. In the Tsallis case, we show that the thermodynamic mass for a Schwarzschild black hole is just a constant multiple of its ADM mass, which is considerably simpler than the approach not utilizing the Jacobson's method.

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