Phase Transition of RN-AdS Black Hole with Fixed Electric Charge and Topological Charge

TL;DR

This paper explores the phase transitions of RN-AdS black holes considering both the cosmological constant as pressure and the spatial curvature as topological charge, revealing Van der Waals-like behavior and analytical coexistence curves.

Contribution

It introduces a novel perspective by treating the spatial curvature as topological charge and derives the corresponding thermodynamic phase transition properties.

Findings

Observation of Van der Waals oscillations in $T-S$ and $P-V$ graphs.

Swallow tail behavior in $G-T$ and $G-P$ graphs.

Analytical phase coexistence curves ($T-P$) consistent with Gibbs free energy analysis.

Abstract

Phase transition of RN-AdS black hole is investigated from a new perspective. Not only the cosmological constant is treated as pressure, but also the spatial curvature of black hole is treated as topological charge. We obtain the extended thermodynamic first law from which the mass is naturally viewed as enthalpy instead of energy. In canonical ensemble with fixed topological charge and electric charge, interesting van der Waals system's oscillatory behavior in $T-S$, $P-V$ graphes and swallow tail behavior in $G-T$, $G-P$ graphes are observed. By applying the Maxwell equal area law and by analysing the gibbs free energy, we obtain analytical phase transition coexistence curves ($T-P$) which are consistent with each other.