Analytic phase structures and thermodynamic curvature for the charged AdS black hole in alternative phase space

TL;DR

This paper explores the phase structure and thermodynamic curvature of charged AdS black holes considering the square of the charge as a thermodynamic variable, revealing van der Waals-like critical behavior and universal properties.

Contribution

It introduces a new phase space framework for charged AdS black holes using the charge squared as a thermodynamic quantity, providing analytical phase diagrams and curvature analysis.

Findings

Charged AdS black holes exhibit van der Waals-type criticality without pressure and volume.

Thermodynamic curvature is positive and consistent across coordinate spaces.

Universal critical exponent is derived from thermodynamic curvature analysis.

Abstract

In this paper, we visit the thermodynamic criticality and thermodynamic curvature of the charged AdS black hole in a new phase space. It is shown that when the square of the total charge of the charged black hole is considered as a thermodynamic quantity, the charged AdS black hole also admits an van der Waals-type critical behavior without the help of thermodynamic pressure and thermodynamic volume. Based on this, we study the fine phase structures of the charged AdS black hole with fixed AdS background in the new framework. On the one hand, we give the phase diagram structures of the charged AdS black hole accurately and analytically, which fills up the gap in dealing with the phase transition of the charged AdS black holes by taking the square of the charge as a thermodynamic quantity. On the other hand, we analyse the thermodynamic curvature of the black hole in two coordinate spaces. The thermodynamic curvatures obtained in two different coordinate spaces are equivalent to each other and are also positive. Based on an empirical conclusion under the framework of thermodynamic geometry, we speculate that when the square of charge is treated as an independent thermodynamic quantity, the charged AdS black hole is likely to present a repulsive between its molecules. More importantly, based on the thermodynamic curvature, we obtain an universal exponent at the critical point of phase transition.