Phase Transition and Critical Phenomena of Charged Einstein-Maxwell-Scalar Black Holes

TL;DR

This paper investigates the phase transition behavior of charged Einstein-Maxwell-scalar black holes, revealing van der Waals-like phenomena, the influence of scalar charge, and complex dependencies of critical parameters, thus deepening understanding of black hole thermodynamics.

Contribution

It provides a comprehensive analysis of phase transitions in EMs black holes, highlighting the scalar charge's dual role and establishing connections with van der Waals systems.

Findings

Black holes exhibit van der Waals-type phase transitions.

Critical exponents match mean field theory predictions.

Scalar charge critically influences phase transition properties.

Abstract

We study the phase transition and critical phenomenon of charged black holes in Einstein-Maxwell-scalar (EMs) theory. Through comprehensive analysis of thermodynamic behaviors manifested in P-V diagrams, G(T,P) surfaces, and C_P curves, we establish that these black holes exhibit van der Waals-type phase transition behavior. The derived critical exponents governing the phase transition show precise correspondence with both van der Waals gas-liquid systems, reinforcing the connection between black hole thermodynamics and mean field theory statistics. The findings reveal a crucial dependence of phase transition properties on the scalar charge parameter. A critical threshold emerges where phase transitions become prohibited when scalar charge exceeds a specific magnitude. However, the transition persists asymptotically as scalar charge approaches zero. The analysis further demonstrates nonlinear relationships between scalar charge and critical parameters: while small scalar charges induce increasing critical volume with charge magnitude, larger values produce an inverse trend. Critical temperature displays complementary behavior, maintaining monotonic variation under certain conditions while exhibiting inverse correlation with critical volume in others. Significantly, the transition points governing critical volume and temperature trends occur at distinct scalar charge values for different black holes, indicating a non-trivial parameter dependence. These results highlight the scalar charge's dual role as both an enabler and suppressor of phase transitions in EMs black holes, providing new insights into the interplay between geometric configurations and thermodynamic properties in modified gravity theories.