High-order QED correction impacts on phase transition of the Euler-Heisenberg AdS black hole

TL;DR

This paper investigates how high-order QED corrections influence the phase transition stability of Euler-Heisenberg AdS black holes, revealing a transition from instability to stability and aligning critical behavior with the van der Waals system.

Contribution

The study re-derives the black hole solution including high-order QED corrections and analyzes its thermodynamic and geometric properties, showing the correction stabilizes phase transitions.

Findings

Only one stable phase transition branch remains after correction.

Critical exponents match those of the van der Waals system.

Scalar curvature analysis shows only one concave surface with correction.

Abstract

Two-phase transition branches of the Euler-Heisenberg (EH) anti-de Sitter (AdS) black hole (BH) were derived from its phase transition critical behavior by Magos et al. [Phys. Rev. D. 102, 084011 (2020)]. We found that the phase transition is unstable. Considering the high-order quantum electrodynamics (QED) correction, we re-derive the EHAdS BH solution and investigate its critical thermodynamic quantities. It is found that the corrected EHAdS BH has only one stable phase transition branch, and its critical exponents are equivalent to that of the vdW system. From the microscopic point of view, we also derive its normalized scalar curvature based on the Ruppeiner geometry. Different from two concave surfaces of the scalar curvature without considering the high-order QED correction, we show that the corrected Ruppeiner geometry has only one concave surface. Our results indicate that the phase transition instability derived by Magos $et~al.$ is due to without considering the high-order QED correction.