The structured pseudospectrum of Schwarzschild black hole
Abstract
The non-Hermitian nature of black hole quasinormal modes (QNMs) can give rise to remarkable spectrum instability. Such instability is naturally characterized by the pseudospectrum for the operator. However, conventional pseudospectrum analyses permit arbitrary operator perturbations that may not correspond to physically admissible modifications. In this work, we introduce the structured pseudospectrum into black hole perturbation theory. We construct two physically motivated perturbation spaces based on effective field theory and the Rezzolla--Zhidenko parametrization, and get their structured pseudospectra using two distinct norms. Our numerical results show that imposing physical constraints substantially reduces the accessible spectrum instability, especially for higher overtones. More importantly, at sufficiently small perturbation scales ε, the structured pseudospectrum around isolated QNMs exhibits approximately elliptical contours with preferred directions that depend on both the mode and the perturbation space, revealing an anisotropic structure beyond the familiar circular behavior of the conventional pseudospectrum.
Related
- Asymptotic expansion of cavity Quasi-Normal Modes in Schwarzschild de-Sitter black hole
- A spinor-adapted geometric approach to nonlinear Dirac systems on the Schwarzschild black hole background
- Nonlinear stability of Schwarzschild black holes for the Einstein-massless Dirac system in spherical symmetry
- Schwarzschild black holes from twistor space
- Threshold Tails of Black hole Differential Observables
BibTeX
@misc{wu2026structured,
title = {{The structured pseudospectrum of Schwarzschild black hole}},
author = {Liang-Bi Wu and Yu-Sen Zhou and Ming-Fei Ji and Xia-Yuan Liu and Libo Xie and Li-Ming Cao},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00853},
eprint = {2611.00853},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00853},
note = {CC0},
}
RIS
TY - UNPB
TI - The structured pseudospectrum of Schwarzschild black hole
AU - Liang-Bi Wu
AU - Yu-Sen Zhou
AU - Ming-Fei Ji
AU - Xia-Yuan Liu
AU - Libo Xie
AU - Li-Ming Cao
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00853
UR - https://arxiv.org/abs/2611.00853
AB - The non-Hermitian nature of black hole quasinormal modes (QNMs) can give rise to remarkable spectrum instability. Such instability is naturally characterized by the pseudospectrum for the operator. However, conventional pseudospectrum analyses permit arbitrary operator perturbations that may not correspond to physically admissible modifications. In this work, we introduce the structured pseudospectrum into black hole perturbation theory. We construct two physically motivated perturbation spaces based on effective field theory and the Rezzolla--Zhidenko parametrization, and get their structured pseudospectra using two distinct norms. Our numerical results show that imposing physical constraints substantially reduces the accessible spectrum instability, especially for higher overtones. More importantly, at sufficiently small perturbation scales ε, the structured pseudospectrum around isolated QNMs exhibits approximately elliptical contours with preferred directions that depend on both the mode and the perturbation space, revealing an anisotropic structure beyond the familiar circular behavior of the conventional pseudospectrum.
ER -