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Quasinormal modes and nonlinear electrodynamics in black hole phase transitions

Zi-Yu Hou1, Yu-Qi Lei1,2,*, and Xian-Hui Ge1,†

  • 1Department of Physics, College of Sciences, Shanghai University, 99 Shangda Road, 200444 Shanghai, China
  • 2Department of Mathematics, College of Sciences, Shanghai University, 99 Shanghai Road, 200444 Shanghai, China

  • *Contact author: yuqi_lei@shu.edu.cn
  • †Contact author: gexh@shu.edu.cn
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Phys. Rev. D 113, 024060 – Published 29 January, 2026

DOI: https://doi.org/10.1103/f333-dnc6

Abstract

We investigate the connection between thermodynamic phase transitions and quasinormal 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 QNM spectrum, we find that the transition point marking the disappearance of the divergence in the QNM 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 a larger angular quantum number l diminishes this correspondence, while a 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.

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Phys. Rev. D 113, 024060– Published 29 January, 2026
  • Received 12 September 2025
  • Accepted 22 December 2025
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