Quasinormal Modes Criticality across Black Hole Extremality
Abstract
We investigate the extremal solution branch to nonextremal branch transition in Einstein-Euler-Heisenberg anti-de Sitter black holes, where the nonlinear electromagnetic parameter λ governs the existence of the extremal branch solution. At fixed pressure and charge, extremal black hole only exist for λ≤λc. For λ>λc, the lowest Hawking temperature keeps nonzero. Near this threshold, the lowest temperature follows a linear critical scaling, Tmin∝(λ−λc)αT. We investigate the corresponding dynamical behavior by computing the quasinormal modes of a massless scalar perturbation along the lowest-temperature black hole branch. As the critical threshold is approached, two complex-frequency quasinormal modes branches collide on the imaginary axis and reorganize into distinct purely imaginary branches. Then the imaginary parts of these modes, together with higher overtones, reach zero at the critical threshold, described by Γn∝(λ−λc)αn, with αn≃αT. The resulting zero-damped modes become increasingly localized near the event horizon, and their relative damping rates closely follow the overtone spacing predicted by the near-horizon AdS2 spectrum. Our results show that the thermodynamic and dynamical critical behavior remain closely connected even when extremal black hole solutions cease to exist, providing further evidence for the relevance of near-extremal spectral behavior in this distinct critical regime.
Related
- Quasinormal modes of Hayward black holes from Schwarzschild to extremality: a comparative spectral analysis
- Quasinormal modes of Kerr-like black bounce spacetime
- Quasinormal modes of massive scalar perturbations in slow-rotation bumblebee black holes with traceless conformal electrodynamics
- Quasinormal modes of rotating black holes with ultralight scalar fields
- Quasinormal modes of a quantum inspired black hole in four dimensions with cosmological constant
BibTeX
@misc{hou2026quasinormal,
title = {{Quasinormal Modes Criticality across Black Hole Extremality}},
author = {Zi-Yu Hou and Yu-Qi Lei and Xian-Hui Ge and Bum-Hoon Lee and Li-Jun Tian},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01869},
eprint = {2611.01869},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01869},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quasinormal Modes Criticality across Black Hole Extremality
AU - Zi-Yu Hou
AU - Yu-Qi Lei
AU - Xian-Hui Ge
AU - Bum-Hoon Lee
AU - Li-Jun Tian
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01869
UR - https://arxiv.org/abs/2611.01869
AB - We investigate the extremal solution branch to nonextremal branch transition in Einstein-Euler-Heisenberg anti-de Sitter black holes, where the nonlinear electromagnetic parameter λ governs the existence of the extremal branch solution. At fixed pressure and charge, extremal black hole only exist for λ≤λ_c. For λ>λ_c, the lowest Hawking temperature keeps nonzero. Near this threshold, the lowest temperature follows a linear critical scaling, T_min∝(λ−λ_c)^α_T. We investigate the corresponding dynamical behavior by computing the quasinormal modes of a massless scalar perturbation along the lowest-temperature black hole branch. As the critical threshold is approached, two complex-frequency quasinormal modes branches collide on the imaginary axis and reorganize into distinct purely imaginary branches. Then the imaginary parts of these modes, together with higher overtones, reach zero at the critical threshold, described by Γ_n∝(λ−λ_c)^α_n, with α_n≃α_T. The resulting zero-damped modes become increasingly localized near the event horizon, and their relative damping rates closely follow the overtone spacing predicted by the near-horizon AdS_2 spectrum. Our results show that the thermodynamic and dynamical critical behavior remain closely connected even when extremal black hole solutions cease to exist, providing further evidence for the relevance of near-extremal spectral behavior in this distinct critical regime.
ER -