Maxwell's equal-area law with several pairs of conjugate variables for RN-AdS black holes

TL;DR

This paper explores the phase transitions of charged AdS black holes using Maxwell's equal-area law with various conjugate variables, revealing new relationships between phase transition points and black hole parameters.

Contribution

It introduces a method to analyze black hole phase transitions with different conjugate variables, enhancing understanding of black hole thermodynamics.

Findings

Phase transition relates to electric potential and horizon radius when charge is fixed.

When cosmological constant is fixed, phase transition depends on the ratio of horizon radius to cosmological constant.

The study provides conditions for choosing conjugate variables in black hole thermodynamics.

Abstract

In this paper, using Maxwell's equal-area law we study the phase transition of charged AdS black holes by choosing different independent conjugate variables. As is well known, the phase transition can be characterized by the state function of the system, the determination of the phase transition point has nothing to do with the choice of independent conjugate variables. To studying the thermodynamic properties of AdS black holes we give the conditions under which the independent conjugate variables are chosen. When the charge of the black hole is invariable, according to the conditions we find that the phase transition is related to the electric potential and the horizon radius of the charged black hole. Keeping the cosmological constant as a fixed parameter, the phase transition of a charged AdS black hole is related to the ratio of the event horizon to cosmological constant of the black hole. This conclusion is of great importance for us to study the critical phenomenon of black holes and to improve the self-consistent geometry theory of black hole thermodynamic.