Spectral instability of black holes: relating the frequency domain to the time domain

Abstract

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 paper we provide further insight into the apparent tension between the frequency-domain and the time-domain descriptions by analyzing the scattering properties of the problem. In the frequency domain, we study analytically the solutions corresponding to the perturbed potential. We show that there are two qualitatively different classes of instabilities, and that both Schwarzschild and Kerr black holes are affected by what we call a "Type II" instability, i.e., an exponential migration of the mode frequencies away from their unperturbed value as the perturbing "bump" moves away from the peak of the unperturbed potential. In the time domain, we elucidate the effect of the spectral instability in terms of the causal structure of the Green's function. By using an equivalent scattering problem we confirm analytically (and show numerically) that the deviation from the unperturbed waveform in the early ringdown stage is proportional to $\epsilon$ when $\epsilon \lesssim 10^{-2}$.

18 pages, 8 figures

References in corpus (30)

• Can environmental effects spoil precision gravitational-wave astrophysics?
• Echoes of ECOs: gravitational-wave signatures of exotic compact objects and of quantum corrections at the horizon scale
• Black holes in galaxies: environmental impact on gravitational-wave generation and propagation
• A recipe for echoes from exotic compact objects
• Matched-filtering and parameter estimation of ringdown waveforms
• Gravitational waves from extreme-mass-ratio systems in astrophysical environments
• Pseudospectrum and black hole quasi-normal mode (in)stability
• Destabilizing the Fundamental Mode of Black Holes: The Elephant and the Flea
• Analysis of Ringdown Overtones in GW150914
• Agnostic black hole spectroscopy: Quasinormal mode content of numerical relativity waveforms and limits of validity of linear perturbation theory
• Gravitational wave signatures of black hole quasi-normal mode instability
• Stability of the fundamental quasinormal mode in time-domain observations against small perturbations
• A multimode quasi-normal spectrum from a perturbed black hole
• Pseudospectrum of horizonless compact objects: a bootstrap instability mechanism
• Perturbing the perturbed: Stability of quasinormal modes in presence of a positive cosmological constant
• Role of black hole quasinormal mode overtones for ringdown analysis
• Spectral (in)stability of quasinormal modes and strong cosmic censorship
• Structural aspects of the anti-de Sitter black hole pseudospectrum
• Quasinormal modes, echoes and the causal structure of the Green's function
• Pseudospectrum of de Sitter black holes
• Quasinormal modes of Schwarzschild black holes on the real axis
• The quasi normal modes of growing dirty black holes
• From black hole spectral instability to stable observables
• Analytic Investigation of the Branch Cut of the Green Function in Schwarzschild Space-time
• Effect of Noise Estimation in Time-Domain Ringdown Analysis: A Case Study with GW150914
• Spectral stability of near-extremal spacetimes
• Black-hole spectroscopy: quasinormal modes, ringdown stability and the pseudospectrum
• Constraints on charged black holes from merger-ringdown signals in GWTC-3 and prospects for the Einstein Telescope
• Regularized calculation of the retarded Green function in Schwarzschild spacetime
• Comparison between time-domain and frequency-domain Bayesian inferences to inspiral-merger-ringdown gravitational-wave signals

Cited by in corpus (8)

• Black hole quasinormal mode resonances
• The (in)stability of quasinormal modes of Boulware-Deser-Wheeler black hole in the hyperboloidal framework
• Pseudospectrum and time-domain analysis of the EFT corrected black holes
• Spectral instability of horizonless compact objects within astrophysical environments
• Exact WKB method for radial Schrödinger equation
• Exploring black holes with multiple photon spheres by interferometric signatures
• Numerical study on the robustness of the stability for stable black holes
• Dynamical system approach to the spectral (in)stability of black holes under localised potential perturbations