Highly Damped Quasinormal Modes of Kerr Black Holes: A Complete Numerical Investigation

TL;DR

This paper presents a comprehensive numerical study of highly damped quasinormal modes of Kerr black holes, revealing that the real part of frequencies approaches a spin-independent constant and detailing the mode structure at high overtones.

Contribution

It introduces a novel numerical method enabling the calculation of very highly damped Kerr black hole modes, extending previous analyses to higher overtones and providing new insights into their asymptotic behavior.

Findings

Real part of frequencies approaches a constant independent of spin and angular index.

Imaginary part of frequencies grows without bound with increasing overtone.

Mode spacing varies monotonically with black hole spin.

Abstract

We compute for the first time very highly damped quasinormal modes of the (rotating) Kerr black hole. Our numerical technique is based on a decoupling of the radial and angular equations, performed using a large-frequency expansion for the angular separation constant_{s}A_{l m}. This allows us to go much further in overtone number than ever before. We find that the real part of the quasinormal frequencies approaches a non-zero constant value which does not depend on the spin s of the perturbing field and on the angular index l: \omega_R=m\varpi(a). We numerically compute \varpi(a). Leading-order corrections to the asymptotic frequency are likely to be of order 1/\omega_I. The imaginary part grows without bound, the spacing between consecutive modes being a monotonic function of a.