Purely imaginary polar resonances of rapidly-rotating Kerr black holes

TL;DR

This paper proves the existence of a unique family of purely imaginary polar quasinormal resonances in rapidly-rotating Kerr black holes, providing an explicit formula and confirming it with numerical data.

Contribution

It introduces an analytical derivation of purely imaginary polar resonances for Kerr black holes, matching recent numerical findings.

Findings

Derived explicit formula for the resonances: w_n=-i2*pi*T_{BH}*(l+1+n)

Confirmed analytical results with recent numerical data

Identified a unique family of non-oscillatory resonances in Kerr black holes

Abstract

We prove the existence of a unique family of non-oscillatory (purely-imaginary) polar quasinormal resonances of rapidly-rotating Kerr black holes. These purely imaginary resonances can be expressed in the compact form: w_n=-i2*pi*T_{BH}*(l+1+n), where T_{BH} is the black-hole temperature, l is the spheroidal harmonic index of the mode, and n=0,1,2,... is the resonance parameter. It is shown that our analytical results for the black-hole resonance spectrum agree with new numerical data that recently appeared in the literature.