Quasi-Normal Modes and Nonlinear Electrodynamics in Black Hole Phase Transitions

TL;DR

This paper explores the link between thermodynamic phase transitions and quasi-normal modes in charged black holes within nonlinear electrodynamics, revealing that QNM behavior encodes thermodynamic phase changes.

Contribution

It demonstrates a precise correspondence between QNM spectrum features and thermodynamic phase transitions in black holes with nonlinear electromagnetic fields.

Findings

QNM slope divergence aligns with heat capacity phase transition points

Larger angular quantum number reduces the QNM-thermodynamics correspondence

Higher overtone number can restore the QNM-thermodynamics link beyond a threshold

Abstract

We investigate the connection between thermodynamic phase transitions and quasi-normal modes (QNMs) in charged black holes with a positive curvature constant, within the framework of $F(R)$-Euler-Heisenberg gravity. Nonlinear electromagnetic fields lead to rich thermodynamic phase structures and significantly affect the QNMs of massless scalar fields. By analyzing the QNMs spectrum, we find that the transition point marking the disappearance of the divergence in the QNMs slope parameter $K$ aligns with the change of the thermodynamic phase structure described by the heat capacity, within the bounds of computational uncertainty. This precise matching holds under variations of the curvature parameter and charge. Furthermore, we show that larger angular quantum number $l$ diminishes this correspondence, while higher overtone number $n$ restores it beyond a threshold. These findings demonstrate that thermodynamic phase transitions of black holes carry embedded dynamical information, uncovering a fundamental link between black hole thermodynamic and dynamical properties.