Thermodynamics of the Euler-Heisenberg-AdS black hole

TL;DR

This paper explores the thermodynamic behavior of Euler-Heisenberg-AdS black holes, revealing phase transitions, critical points, and the impact of nonlinear electromagnetic effects on black hole thermodynamics.

Contribution

It generalizes black hole solutions in Euler-Heisenberg theory with a cosmological constant and analyzes their thermodynamic properties, including phase transitions and critical phenomena.

Findings

Identified two black hole phases with distinct electromagnetic behaviors.

Established the existence of phase transitions and coexistence curves.

Confirmed critical exponents match mean field theory predictions.

Abstract

We generalize the solution to the Euler-Heisenberg (EH) theory coupled to gravity that represents a nonlinearly charged static black hole (BH) introducing the cosmological constant; the obtained solution is characterized by four parameters: mass $M$, electric charge $Q$, cosmological constant $\Lambda$ (positive or negative) and the Euler-Heisenberg theory parameter $a$. Then we briefly analyze some BH features like horizons, electromagnetic field and geodesics. We mainly focus on its thermodynamic properties in the extended space where the anti-de Sitter parameter is interpreted as the pressure; we show the consistency between the Smarr formula and the first law of BH thermodynamics, interpreting the parameter of the EH theory as the vacuum polarization. We determine the equation of state and the critical points; the critical volume determines two branches of BHs, one near Maxwell behavior and a second one manifestly nonlinear electromagnetic. Moreover, the analysis of the Gibbs free energy indicates that two phase transitions can occur; we also construct the coexistence curve $P$-$T$ where the different phases of the BH can be observed; the critical point is characterized by the standard mean field theory exponents, and the critical variables satisfy $P_{\rm crit} v_{\rm crit}/ T_{\rm crit} = 3/8 $ plus terms of the ten thousandths order in the Euler-Heisenberg parameter $a$