Thermodynamics of Kerr-Sen-AdS black holes in the restricted phase space

TL;DR

This paper explores the thermodynamics of Kerr-Sen-AdS black holes within a restricted phase space framework, revealing phase transition behaviors and suggesting a possible universality in black hole thermodynamics.

Contribution

It introduces a novel restricted phase space thermodynamics formalism for Kerr-Sen-AdS black holes, excluding the $PdV$ term, and investigates their phase transition properties.

Findings

Identifies phase transition behavior in the free energy and conjugate variables.

Shows the thermodynamics of Kerr-Sen-AdS black holes resemble that of Reissner-Nordström-AdS and Kerr-AdS black holes.

Suggests a universal aspect of phase transition behavior in black hole thermodynamics.

Abstract

We analyse the restricted phase space thermodynamics (RPST) of Kerr-Sen-AdS black holes with the central charge $C$ and its conjugate chemical potential $\mu$ but exclude the familiar $PdV$ term in the first law of black hole thermodynamics. That gives rise to a new perspective on the thermodynamics of black holes. Using the scaling properties, we investigate the first law and the corresponding Euler formula. Such formalism has its beauty, to say, for example, the mass is considered to be a homogeneous function of the extensive variables in the first order. In contrast, the intensive variables are of zeroth order. Because of the complicated expressions of the metric, we numerically calculate the critical values of the thermodynamic quantities. We find the phase transition behaviour of the free energy and other thermodynamic conjugate variables that appear in the first law. The RPST of the Kerr-Sen-AdS black holes is like that of the Reissner-Nordstr$\ddot{o}$m-AdS and the Kerr-AdS black holes. Such notions of the phase transition behaviour show that there should be some underlying universality in the RPST formalism.