Hyperboloidal Approach to Quasinormal Modes

Abstract

Oscillations of black hole spacetimes exhibit divergent behavior toward the bifurcation sphere and spatial infinity. This divergence can be understood as a consequence of the geometry in these spacetime regions. In contrast, black-hole oscillations are regular when evaluated toward the event horizon and null infinity. Hyperboloidal surfaces naturally connect these regions, providing a geometric regularization of time-harmonic oscillations called quasinormal modes (QNMs). This review traces the historical development of the hyperboloidal approach to QNMs. We discuss the physical motivation for the hyperboloidal approach and highlight current developments in the field.

Mini-Review to topic collection "Quasi-Normal Modes, Non-Selfadjoint Operators and Pseudospectrum: an Interdisciplinary Approach"

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Cited by in corpus (10)

• Quasinormal modes of black holes embedded in halos of matter
• The Confluent Heun functions in Black Hole Perturbation Theory: a spacetime interpretation
• Quasi-normal mode expansions of black hole perturbations: a hyperboloidal Keldysh's approach
• Pseudospectrum of rotating analog black holes
• Dynamical quasinormal mode excitation
• Probing the Unstable Spectrum of Schwarzschild-like Black Holes
• Spectral instability of horizonless compact objects within astrophysical environments
• Numerical Evidence for Non-Axisymmetric Gravitational "Hair" for Extremal Kerr Black Hole Spacetimes with Hyperboloidal Foliations
• QNM families: classification and competition
• Black hole destabilization via trapped quasi-normal modes