From black hole spectral instability to stable observables

Abstract

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 instability will be a technical challenge. Here we investigate the spectral instability of time-independent data. This leads us to study the Regge Poles (RP), the counterparts to the QNMs in the complex angular momentum plane. We present evidence that the RP spectrum is unstable but that not all overtones are affected equally by this instability. In addition, we reveal that behind this spectral instability lies an underlying structure. The RP spectrum is perturbed in such a way that one can still recover stable scattering quantities using the complex angular momentum approach. Overall, the study proposes a novel and complementary approach on the black hole spectral instability phenomena which allows us to reveal a surprising and unexpected mechanism at play which protects scattering quantities from the instability.

arXiv comment5 + 3 pages, 4 + 2 figures, 1 table. Title changed. Matches the accepted version in Phys. Rev. Lett

References in corpus (34)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• Quasinormal modes of black holes and black branes
• Non-Hermitian Physics
• Quasinormal modes of black holes: from astrophysics to string theory
• Geodesic stability, Lyapunov exponents and quasinormal modes
• On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA
• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Can environmental effects spoil precision gravitational-wave astrophysics?
• Black Hole Spectroscopy: Testing General Relativity through Gravitational Wave Observations
• Testing the no-hair theorem with GW150914
• Spectroscopy of Kerr black holes with Earth- and space-based interferometers
• Connection between black-hole quasinormal modes and lensing in the strong deflection limit
• Bayesian model selection for testing the no-hair theorem with black hole ringdowns
• Pseudospectrum and black hole quasi-normal mode (in)stability
• Destabilizing the Fundamental Mode of Black Holes: The Elephant and the Flea
• Quantifying excitations of quasinormal mode systems
• Universality of high-energy absorption cross sections for black holes
• Scattering and absorption of gravitational plane waves by rotating black holes
• Gravitational wave signatures of black hole quasi-normal mode instability
• The imprint of the equation of state on the axial w-modes of oscillating neutron stars
• Environmental Effects for Gravitational-wave Astrophysics
• Unstable circular null geodesics of static spherically symmetric black holes, Regge poles and quasinormal frequencies
• Connection Between the Shadow Radius and Quasinormal Modes in Rotating Spacetimes
• Stability of the fundamental quasinormal mode in time-domain observations against small perturbations
• Nonlinear effects in the black hole ringdown: absorption-induced mode excitation
• Energy scales and black hole pseudospectra: the structural role of the scalar product
• Fine structure of high-energy absorption cross sections for black holes
• Complex angular momentum in black hole physics and quasinormal modes
• Strong gravitational lensing and black hole quasinormal modes: Towards a semiclassical unified description
• Regge pole description of scattering of scalar and electromagnetic waves by a Schwarzschild black hole
• Rainbow scattering in the gravitational field of a compact object
• Scattering from compact objects: Regge poles and the complex angular momentum method
• An alternative description of gravitational radiation from black holes based on the Regge poles of the $\mathcal{S}$-matrix and the associated residues
• Regge pole description of scattering by dirty black holes

Cited by in corpus (11)

• Ringdown stability: greybody factors as stable gravitational-wave observables
• Quasinormal modes and greybody factor of a Lorentz-violating black hole
• Pseudospectra of Holographic Quasinormal Modes
• Structural aspects of the anti-de Sitter black hole pseudospectrum
• Spectral instability of black holes: relating the frequency domain to the time domain
• The (in)stability of quasinormal modes of Boulware-Deser-Wheeler black hole in the hyperboloidal framework
• Spectral instability of horizonless compact objects within astrophysical environments
• Natural polynomials for Kerr quasi-normal modes
• Exploring black holes with multiple photon spheres by interferometric signatures
• Excitation factors for horizonless compact objects: long-lived modes, echoes, and greybody factors
• Dynamical system approach to the spectral (in)stability of black holes under localised potential perturbations