Spectral instability of parametrized black hole quasinormal modes in the high-overtone limit via the exact WKB analysis

Abstract

We study the asymptotic behavior of parametrized black hole quasinormal modes (QNMs) in the high-overtone limit. To gain insights into their analytical structure, we apply the exact WKB method, which was recently developed by the same authors. Our theoretical predictions are confirmed in good agreement with the numerical results based on Leaver's method. For specific values of parametrization parameters that characterize deviations from general relativity, we find that the real part of asymptotic QNM frequencies diverges in the high-overtone limit, in sharp contrast to the case of a Schwarzschild black hole. This demonstrates that the convergence of the real parts of high-overtone QNMs is a distinctive feature of general relativity, while parametrized corrections generically lead to divergent spectral behaviors.

26 pages, 8 figures

References in corpus (14)

• Can environmental effects spoil precision gravitational-wave astrophysics?
• The physical interpretation of the spectrum of black hole quasinormal modes
• Destabilizing the Fundamental Mode of Black Holes: The Elephant and the Flea
• Gravitational wave signatures of black hole quasi-normal mode instability
• Stability of the fundamental quasinormal mode in time-domain observations against small perturbations
• Analytic Study of Rotating Black-Hole Quasinormal Modes
• Asymptotic Spectroscopy of Rotating Black Holes
• Spectral Method for the Gravitational Perturbations of Black Holes: Schwarzschild Background Case
• Theory-agnostic Reconstruction of Potential and Couplings from Quasi-Normal Modes
• Constraining modifications of black hole perturbation potentials near the light ring with quasinormal modes
• Quasi-normal modes of non-separable perturbation equations: the scalar non-Kerr case
• Parametrized Black Hole Quasinormal Ringdown Formalism for Higher Overtones
• Existence and Uniqueness of Exact WKB Solutions for Second-Order Singularly Perturbed Linear ODEs
• Exact Solutions for the Singularly Perturbed Riccati Equation and Exact WKB Analysis