Pole Skipping, Avoided Crossing, and Resonant Excitation in Kerr Quasinormal Modes near Algebraically Special Frequencies

TL;DR

This paper explains long-standing anomalies in Kerr quasinormal modes near special frequencies by analyzing pole behaviors, revealing avoided crossings and pole skipping as key phenomena.

Contribution

It provides a detailed explanation of anomalous behaviors in Kerr quasinormal modes, connecting them to avoided crossings and pole skipping mechanisms.

Findings

Bifurcation is due to avoided crossing with resonant excitation.

Disappearance results from pole skipping caused by pole-zero cancellation.

Resolves decades-old puzzles about Kerr quasinormal mode anomalies.

Abstract

Kerr quasinormal modes near algebraically special frequencies exhibit anomalous behavior, including apparent bifurcation, disappearance, and a nonsmooth connection to the Schwarzschild limit, which has remained puzzling for decades. Tracking poles and zeros of Green-function building blocks across different Riemann sheets, we show that the bifurcation is due to an avoided crossing accompanied by resonant excitation, while the disappearance is due to pole skipping caused by cancellation of a quasinormal-mode pole by a Matsubara-mode zero. This resolves the physical origin of these long-standing anomalies.