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

TL;DR

This paper investigates the high-overtone behavior of parametrized black hole quasinormal modes using the exact WKB method, revealing divergence in frequencies for deviations from general relativity, contrasting with Schwarzschild black holes.

Contribution

The authors apply the exact WKB analysis to parametrized black hole QNMs, providing new analytical insights and confirming predictions with numerical methods, highlighting divergence phenomena.

Findings

Real parts of QNM frequencies diverge for certain parameters in high-overtone limit.

Convergence of high-overtone QNMs is unique to general relativity.

Parametrized deviations lead to divergent spectral behaviors in black hole QNMs.

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.