Extended phase space thermodynamics and $P-V$ criticality of charged black holes in Brans-Dicke theory

TL;DR

This paper explores the thermodynamics of charged black holes within Brans-Dicke theory, revealing Van der Waals-like phase transitions and critical behavior in an extended phase space framework.

Contribution

It introduces the analysis of black hole thermodynamics in Brans-Dicke theory considering the cosmological constant as pressure, highlighting phase transition phenomena.

Findings

Identification of critical points in thermodynamic phase space

Demonstration of Van der Waals-like phase transitions

Plots of $P-r_{+}$ and $G-T$ diagrams showing phase behavior

Abstract

In this paper, taking in to account Brans-Dick theory, we investigate thermodynamic behavior of charged black hole solutions. We study the analogy of the black hole solution with the Van der Waals liquid-gas system in the extended phase space by considering the cosmological constant as dynamical pressure. We obtain critical values of thermodynamic coordinates and plot $P-r_{+}$ and $G-T$ diagrams to study the phase transition.