A mystery of black-hole gravitational resonances

TL;DR

This paper investigates a significant discrepancy between analytical predictions and numerical results for gravitational resonant frequencies of rapidly-rotating Kerr black holes, challenging recent claims about the validity of existing resonance equations.

Contribution

It identifies and discusses a key discrepancy between analytical and numerical results for Kerr black hole resonances, refuting recent claims about the resonance equation's validity in certain regimes.

Findings

Discrepancy between Detweiler's analytical formula and numerical results.

Refutation of claims that the resonance equation is invalid for damped resonances.

Highlighting the 'black-hole quasinormal mystery' in Kerr black hole spectra.

Abstract

More than three decades ago, Detweiler provided an analytical formula for the gravitational resonant frequencies of rapidly-rotating Kerr black holes. In the present work we shall discuss an important discrepancy between the famous {\it analytical} prediction of Detweiler and the recent {\it numerical} results of Zimmerman et. al. In addition, we shall refute the claim that recently appeared in the physics literature that the Detweiler-Teukolsky-Press resonance equation for the characteristic gravitational eigenfrequencies of rapidly-rotating Kerr black holes is not valid in the regime of damped quasinormal resonances with $\Im\omega/T_{\text{BH}}\gg1$ (here $\omega$ and $T_{\text{BH}}$ are respectively the characteristic quasinormal resonant frequency of the Kerr black hole and its Bekenstein-Hawking temperature). The main goal of the present paper is to highlight and expose this important {\it black-hole quasinormal mystery} (that is, the intriguing discrepancy between the analytical and numerical results regarding the gravitational quasinormal resonance spectra of rapidly-rotating Kerr black holes).