Quasinormal resonances of near-extremal Kerr-Newman black holes

TL;DR

This paper derives an analytical formula for the fundamental quasinormal mode frequencies of near-extremal Kerr-Newman black holes, relating them to black hole parameters like temperature and angular velocity.

Contribution

It provides the first simple analytic expression for these resonances, valid in the near-extremal, slowly rotating regime, linking mode frequencies to black hole physical parameters.

Findings

Derived an explicit formula for quasinormal frequencies

Validated the formula within the specified regime

Connected mode properties to black hole thermodynamics

Abstract

We study analytically the fundamental resonances of near-extremal, slowly rotating Kerr-Newman black holes. We find a simple analytic expression for these black-hole quasinormal frequencies in terms of the black-hole physical parameters: omega=m Omega-2i pi T(l+1+n), where T and Omega are the temperature and angular velocity of the black hole. The mode parameters l and m are the spheroidal harmonic index and the azimuthal harmonic index of a co-rotating mode, respectively. This analytical formula is valid in the regime Im omega << Re omega <<1/M, where M is the black-hole mass.