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It was recently pointed out that the fundamental mode of the Regge-Wheeler effective potential is unstable against an insignificant Gaussian metric perturbation, which, in turn, might substantially challenge the black hole spectroscopy.…

General Relativity and Quantum Cosmology · Physics 2026-02-06 Shui-Fa Shen , Guan-Ru Li , Ramin G. Daghigh , Jodin C. Morey , Michael D. Green , Qiyuan Pan , Cheng-Gang Shao , Wei-Liang Qian

Owing to its substantial implications for black hole spectroscopy, spectral instability has attracted considerable attention in the literature. While the emergence of such instability is attributed to the non-Hermitian nature of the…

General Relativity and Quantum Cosmology · Physics 2025-12-23 Shui-Fa Shen , Guan-Ru Li , Ramin G. Daghigh , Jodin C. Morey , Michael D. Green , Wei-Liang Qian , Rui-Hong Yue

We elaborate on a criterion for the emergence of instability in the fundamental mode recently observed by Cheung {\it et al.}, as a universal phenomenon in the context of black hole perturbations. Such instability is characterized by an…

General Relativity and Quantum Cosmology · Physics 2024-12-20 Wei-Liang Qian , Guan-Ru Li , Ramin G. Daghigh , Stefan Randow , Rui-Hong Yue

We present a short review of the analytical aspects of recent progress in the study of black hole spectral instability and its potential observational consequences. This topic, inspired by earlier foundational works, has attracted…

General Relativity and Quantum Cosmology · Physics 2026-01-13 Shui-Fa Shen , Guan-Ru Li , Ramin G. Daghigh , Jodin C. Morey , Michael D. Green , Wei-Liang Qian , Rui-Hong Yue

The aim of this work is to improve understanding of the resonant spectra of black holes under perturbations arising from e.g. compact objects or accretion disks in their vicinity. It is known that adding a weak perturbation to the radial…

General Relativity and Quantum Cosmology · Physics 2026-01-09 T. Torres , S. R. Dolan

Black hole spectroscopy with gravitational waves is an important tool to measure the mass and spin of astrophysical black holes and to test their Kerr nature. Next-generation ground- and space-based detectors will observe binary black hole…

General Relativity and Quantum Cosmology · Physics 2022-10-26 Emanuele Berti , Vitor Cardoso , Mark Ho-Yeuk Cheung , Francesco Di Filippo , Francisco Duque , Paul Martens , Shinji Mukohyama

This paper numerically studies if the stability of a stable black hole is robust against the small perturbation on geometry near its event horizon. As a toy model, it encodes the such perturbation into deformations of Regge-Wheeler…

General Relativity and Quantum Cosmology · Physics 2025-09-09 Zhan-Feng Mai , Run-Qiu Yang

The quasi-normal mode (QNM) spectrum of black holes is unstable under small perturbation of the potential and has observational consequences in time signals. Such signals might be experimentally difficult to observe and probing this…

General Relativity and Quantum Cosmology · Physics 2023-09-14 Theo Torres

Recent non-modal analyses have uncovered spectral instabilities in the quasinormal-mode spectrum of black holes; a phenomenon that intriguingly extends to spherically-symmetric exotic compact objects. These results point to a sensitivity of…

General Relativity and Quantum Cosmology · Physics 2026-02-11 Kyriakos Destounis , Mateus Malato Corrêa , Caio F. B. Macedo , Rodrigo Panosso Macedo

Recent work applying the notion of pseudospectrum to gravitational physics showed that the quasinormal mode spectrum of black holes is unstable, with the possible exception of the longest-lived (fundamental) mode. The fundamental mode…

General Relativity and Quantum Cosmology · Physics 2022-03-29 Mark Ho-Yeuk Cheung , Kyriakos Destounis , Rodrigo Panosso Macedo , Emanuele Berti , Vitor Cardoso

Recent work has shown that the quasinormal mode spectrum of black holes is unstable under small perturbations (of order $\epsilon$) of the radial potential, while the early time-domain ringdown waveform is only marginally affected. In this…

General Relativity and Quantum Cosmology · Physics 2024-10-10 Yiqiu Yang , Zhan-Feng Mai , Run-Qiu Yang , Lijing Shao , Emanuele Berti

It has been shown, via specific examples and a pseudospectrum analysis, that the black hole quasinormal spectra are unstable. The implication of such a result for gravitational-wave physics and of our understanding of black holes is, still,…

General Relativity and Quantum Cosmology · Physics 2024-04-03 Vitor Cardoso , Shilpa Kastha , Rodrigo Panosso Macedo

Black hole dynamical instabilities have been mostly studied in specific models. We here study the general properties of the complex-frequency modes responsible for such instabilities, guided by the example of a charged scalar field in an…

General Relativity and Quantum Cosmology · Physics 2016-07-04 Antonin Coutant , Florent Michel , Renaud Parentani

In this work we explore some aspects of the spectral instability of back hole quasi-normal modes, using a specific model as an example. The model is that of a small bump perturbation to the effective potential of linear axial gravitational…

General Relativity and Quantum Cosmology · Physics 2025-01-08 Valentin Boyanov

In this work, we wish to address the question -- whether the quasi-normal modes, the characteristic frequencies associated with perturbed black hole spacetimes, central to the stability of these black holes, are themselves stable. Though…

General Relativity and Quantum Cosmology · Physics 2023-11-07 Subhodeep Sarkar , Mostafizur Rahman , Sumanta Chakraborty

In this work, we investigate the relation between bound states and quasinormal modes within black hole perturbation theory in the context of spectral instability. Our analysis indicates that the reliability of such spectral mapping…

General Relativity and Quantum Cosmology · Physics 2026-04-01 Guan-Ru Li , Wei-Liang Qian , Xiao-Mei Kuang , Ramin G. Daghigh , Jodin C. Morey , Michael D. Green , Peng Xu , Rui-Hong Yue

Recent studies have shown that a secondary potential barrier, forming a potential well outside the event horizon, can destabilize the Quasinormal Mode (QNM) spectrum of black holes. We find that spectral instability may persist even after…

General Relativity and Quantum Cosmology · Physics 2026-03-09 Peng Wang , Tianshu Wu

Black hole spectroscopy is a powerful tool to probe the Kerr nature of astrophysical compact objects and their environment. The observation of multiple ringdown modes in gravitational waveforms could soon lead to high-precision…

General Relativity and Quantum Cosmology · Physics 2021-10-27 Kyriakos Destounis , Rodrigo Panosso Macedo , Emanuele Berti , Vitor Cardoso , José Luis Jaramillo

Recent investigations of the pseudospectrum in black hole spacetimes have shown that quasinormal mode frequencies suffer from spectral instabilities. This phenomenon may severely affect gravitational-wave spectroscopy and limit precision…

General Relativity and Quantum Cosmology · Physics 2023-03-13 Valentin Boyanov , Kyriakos Destounis , Rodrigo Panosso Macedo , Vitor Cardoso , José Luis Jaramillo

The quasinormal mode spectrum of black holes is unstable against small modifications of the radial potential describing massless perturbations. We study how these small modifications affect the convergence of the quasinormal mode expansion…

General Relativity and Quantum Cosmology · Physics 2025-03-28 Naritaka Oshita , Emanuele Berti , Vitor Cardoso
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