# Novel equal area law and analytical charge-electric potential criticality for charged Anti-de Sitter black holes

## TL;DR

This paper analytically investigates the phase transitions and critical phenomena of charged Anti-de Sitter black holes using a novel equal area law approach in the charge-electric potential plane, revealing distinct behaviors near and far from the critical point.

## Contribution

It introduces a new analytical equal area law for charge-electric potential criticality and derives the phase diagram for charged AdS black holes.

## Key findings

- Two different expressions of the equal area law near and far from the critical point.
- Analytical coexistence curves for low and high electric potential phases.
- Detailed phase diagram and critical phenomena analysis in the charge-electric potential plane.

## Abstract

We study the equal area law and charge-electric potential criticality for the charged Anti-de Sitter black holes. Considering that the black hole charge is a double-valued function of the electric potential, we investigate the equal area law in detail. We find that the equal area law has two different expressions when the thermodynamic quantities are near the critical point and far from the critical point. For these two different cases, we obtain the analytical coexistence curve for the low and high electric potential black hole phases by using these two expressions of the equal area law. Based on the result, we analytically study the phase diagram and the critical phenomena in the charge-electric potential plane.