Complex Plane Phase Diagram and Widom Line for the Born-Infeld Black Holes with Reentrant Phase Transition

TL;DR

This paper explores the complex phase diagram and Widom line of Born-Infeld AdS black holes, revealing how nonlinear effects influence phase transitions and uncovering universal thermodynamic features in supercritical regimes.

Contribution

The study extends Lee-Yang zeros analysis to Born-Infeld AdS black holes, deriving their complex phase diagram and supercritical crossover line, highlighting the impact of nonlinear effects on phase behavior.

Findings

Born-Infeld nonlinear effects alter phase transition characteristics.

The Widom line remains unique in the supercritical region.

Universal features of thermodynamics in nonlinear gravitational systems are identified.

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 Lee-Yang zeros, we obtained the complex phase diagram of the Born-Infeld AdS black hole and derived the supercritical crossover line -- Widom line, which 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.