Thermodynamic Complex Phase Diagram for the Born-Infeld AdS Black Holes with Reentrant Phase Transition

TL;DR

This work analyzes the thermodynamics of four-dimensional Born-Infeld AdS black holes in extended phase space, focusing on how nonlinear BI electrodynamics modifies phase structure, including reentrant transitions. By applying Lee-Yang zeros and extending the horizon radius into the complex plane, the authors construct complete complex phase diagrams for three representative BI parameters $b$, identifying coexistence and spinodal lines and extracting a Widom line that marks the liquidlike-to-gaslike crossover in the supercritical regime. A key finding is that, regardless of rich critical-region behavior, there exists a single Widom line in the supercritical region that emanates from the stable critical point of the first-order transition; zeroth-order transitions do not produce a Widom line. These results illuminate the connection between critical phenomena and black hole thermodynamics in nonlinear gravity and suggest a universal feature of supercritical behavior in BI-AdS systems.

Abstract

The Lee-Yang phase transition theory applied in the anti-de Sitter (AdS) black hole has inspired the exploration of complex phase diagram and supercritical phenomena in black hole thermodynamics. In this study, we extend the approach to the four dimensional Born-Infeld AdS black hole. This system exhibits a rich phase structure, including reentrant phase transitions, due to the modulation of the Born-Infeld nonlinear parameter. Through the analysis by Lee-Yang zeros, we obtained the complex phase diagram of the Born-Infeld AdS black hole and derived the supercritical crossover line -- Widom line. It strictly originates from the first-order stable critical point. The results indicate that Born-Infeld nonlinear effects significantly alter the types and characteristics of phase transition in critical region, while do not disrupt the uniqueness of the Widom line in supercritical region. Our study uncovers a universal simplified feature of the thermodynamic behavior of nonlinear gravitational systems in supercritical region. It also deepens our understanding of the fundamental connection between critical phenomena and continuous phase transitions in the extended phase space of black holes.

Figures (8)

• Figure 1: Phase diagrams of BI-AdS black hole with $b=0.4$ and in the left diagram we set $P=0.98P_z$.
• Figure 2: Phase diagrams of BI-AdS black hole with $b=1.0$ and in the left diagram we set $P=0.5P_c$.
• Figure 3: Singularities distribution of the Gibbs free energy for the BI-AdS black hole at $b=0.4$.
• Figure 4: Complex phase diagram of BI-AdS black hole at $b=0.4$.
• Figure 5: Singularities distribution of the four dimensional BI-AdS black hole at $b=0.45$.