Clapeyron equations and fitting formula of the coexistence curve in the extended phase space of charged AdS black holes

TL;DR

This paper reviews and generalizes Clapeyron equations and equal area laws in the extended phase space of charged AdS black holes, providing a highly accurate coexistence curve fitting formula that enhances understanding of black hole thermodynamics.

Contribution

It introduces generalized Clapeyron equations, explores charge independence of the coexistence curve, and presents a precise fitting formula for the coexistence curve in charged AdS black holes.

Findings

Maxwell's equal area law applies in multiple oscillatory lines.

The coexistence curve is charge independent in reduced parameters.

The fitting formula matches well with calculated Clapeyron values.

Abstract

In this paper, we first review the equal area laws and Clapeyron equations in the extended phase space of the charged anti-de Sitter black holes. With different fixed parameters, the Maxwell's equal area law holds not only in the pressure-thermodynamic volume oscillatory line, but also in the charge-electric potential and temperature-entropy oscillatory lines. The conventional Clapeyron equation is generalized and two extra equations are found. Moreover, we show that the coexistence curve of the small and large charged black holes is charge independent in the reduced parameter space for any dimension of spacetime. The highly accurate fitting formula for the coexistence curve is also presented. Using this fitting formula of the coexistence curve, we find that the Clapeyron equations are highly consistent with the calculated values. The fitting formula is also very useful for further study on the thermodynamic property of the system varying along the coexistence curve.