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.

11 pages. v3: More clarifications and new references

References in corpus (5)

• Phase transition and Thermodynamical geometry of Reissner-Nordström-AdS Black Holes in Extended Phase Space
• Restricted phase space thermodynamics for AdS black holes via holography
• Chemical Potential in the First Law for Holographic Entanglement Entropy
• Thermodynamics of Kerr-AdS black holes in the restricted phase space
• Critical phenomena and chemical potential of charged AdS black hole

Cited by in corpus (4)

• Restricted phase space thermodynamics for AdS black holes via holography
• Thermodynamics of Kerr-AdS black holes in the restricted phase space
• Thermodynamics for higher dimensional rotating black holes with variable Newton constant
• Restricted phase space thermodynamics for black holes in higher dimensions and higher curvature gravities