Restricted phase space thermodynamics for AdS black holes via holography

TL;DR

The paper introduces a new restricted phase space thermodynamics formalism for AdS black holes that fixes the AdS radius, incorporating central charge and chemical potential as conjugate variables, and verifies it with RN-AdS black holes.

Contribution

It proposes a novel thermodynamic framework for AdS black holes that omits the traditional pressure-volume variables and includes central charge and chemical potential, ensuring thermodynamic consistency.

Findings

The formalism satisfies the Euler relation and Gibbs-Duhem equation.

Application to RN-AdS black holes reveals unique thermodynamic behaviors.

The approach simplifies black hole thermodynamics by fixing the AdS radius.

Abstract

A new formalism for thermodynamics of AdS black holes called the {\em restricted phase space thermodynamics} (RPST) is proposed. The construction is based on top of Visser's holographic thermodynamics, but with the AdS radius fixed as a constant. Thus the RPST is free of the $(P,V)$ variables but inherits the central charge and chemical potential as a new pair of conjugate thermodynamic variables. In this formalism, the Euler relation and the Gibbs-Duhem equation hold simultaneously with the first law of black hole thermodynamics, which guarantee the appropriate homogeneous behaviors for the black hole mass and the intensive variables. The formalism is checked in detail in the example case of 4-dimensional RN-AdS black hole in Einstein-Maxwell theory, in which some interesting thermodynamic behaviors are revealed.