Branching of quasinormal modes for nearly extremal Kerr black holes

TL;DR

This paper reveals that nearly extremal Kerr black holes exhibit two distinct types of quasinormal modes, zero-damping modes and damped modes, which merge as the black hole spin decreases, providing new insights into black hole perturbation spectra.

Contribution

The study identifies and characterizes two separate families of quasinormal modes in nearly extremal Kerr black holes, explaining their branching behavior and spectral properties.

Findings

ZDMs exist for all harmonic indices with frequencies clustering on the real axis.

Damped modes exist for counterrotating modes and certain corotating modes with specific parameters.

ZDMs and DMs merge into a single spectrum as the black hole spin decreases.

Abstract

We show that nearly extremal Kerr black holes have two distinct sets of quasinormal modes, which we call zero-damping modes (ZDMs) and damped modes (DMs). The ZDMs exist for all harmonic indices $l$ and $m \ge 0$, and their frequencies cluster onto the real axis in the extremal limit. The DMs have nonzero damping for all black hole spins; they exist for all counterrotating modes ($m<0$) and for corotating modes with $0\leq \mu\lesssim \mu_c=0.74$ (in the eikonal limit), where $\mu\equiv m/(l+1/2)$. When the two families coexist, ZDMs and DMs merge to form a single set of quasinormal modes as the black hole spin decreases. Using the effective potential for perturbations of the Kerr spacetime, we give intuitive explanations for the absence of DMs in certain areas of the spectrum and for the branching of the spectrum into ZDMs and DMs at large spins.