Black hole thermodynamics is extensive with variable Newton constant

Abstract

Inspired by the recent studies on the thermodynamics of AdS black holes in the restricted phase space formalism, we propose a similar formalism for the thermodynamics of non-AdS black holes with variable Newton constant. It is shown that, by introducing the new variables $N,\mu$, where $N$ is proportional to the inverse Newton constant and $\mu$ its conjugate variable, referred to as the chemical potential, the black hole thermodynamics can be formulated in a form which is consistent with the standard extensive thermodynamics for open macroscopic systems, with the first law and the Euler relation hold simultaneously. This formalism has profound implications, in particular, the mass is a homogeneous function of the first order in the extensive variables and the intensive variables are zeroth order homogeneous functions. The chemical potential is shown to be closely related to the Euclidean action evaluated at the black hole configuration.

arXiv comment11 pages. v3: More clarifications and new references

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• Thermodynamic topology of black Holes in f(R) gravity
• Bulk-boundary and RPS Thermodynamics from Topology perspective
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• Restricted phase space thermodynamics for black holes in higher dimensions and higher curvature gravities
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• Thermodynamics of Flat 4D Einstein-Gauss-Bonnet Black Hole with Rényi Entropy: An RPST-like formalism
• RPST-Inspired Formalism for Black Holes in Flat Spacetime