Dynamical instabilities and quasi-normal modes, a spectral analysis with applications to black-hole physics

Abstract

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 electrostatic potential. We show that these modes are square integrable, have a vanishing conserved norm, and appear in mode doublets or quartets. We also study how they appear in the spectrum and how their complex frequencies subsequently evolve when varying some external parameter. When working on an infinite domain, they appear from the reservoir of quasi-normal modes obeying outgoing boundary conditions. This is illustrated by generalizing, in a non-positive definite Krein space, a solvable model (Friedrichs model) which originally describes the appearance of a resonance when coupling an isolated system to a mode continuum. In a finite spatial domain instead, they arise from the fusion of two real frequency modes with opposite norms, through a process that closely resembles avoided crossing.

31 pages, 13 figures. Small clarifications, title changed, matches published version

References in corpus (12)

• Explosion and final state of an unstable Reissner-Nordstrom black hole
• Instabilities of Black Strings and Branes
• Slow relaxation of rapidly rotating black holes
• Classical instability of Kerr-AdS black holes and the issue of final state
• Nonlinear Evolution and Final Fate of Charged Anti-de Sitter Black Hole Superradiant Instability
• Holographic End-Point of Spatially Modulated Phase Transition
• Superradiant instability of black holes immersed in a magnetic field
• Resonant Hawking radiation in Bose-Einstein condensates
• Non-linear effects in time-dependent transonic flows: An analysis of analogue black hole stability
• Time-dependent study of a black-hole laser in a flowing atomic condensate
• Bifurcation of the quasinormal spectrum and Zero Damped Modes for rotating dilatonic black holes
• Condition for emergence of complex eigenvalues in the Bogoliubov-de Gennes equations

Cited by in corpus (8)

• Detecting Rotational Superradiance in Fluid Laboratories
• Ergoregion instabilities in rotating two-dimensional Bose--Einstein condensates: new perspectives on the stability of quantized vortices
• Quantum vacuum excitation of a quasi-normal mode in an analog model of black hole spacetime
• Is a doubly quantized vortex dynamically unstable in uniform superfluids?
• Holographic dissipative space-time supersolids
• Four-wave mixing and enhanced analogue Hawking effect in a nonlinear optical waveguide
• Quasi-normal modes and fermionic vacuum decay around a Kerr black hole
• Acoustic horizons and the Hawking effect in polariton fluids of light