Ergodic Hysteresis of the Kerr black hole spectrum

TL;DR

This paper reveals a complex non-Hermitian structure in Kerr black hole spectra, showing a cascade of exceptional points that enable mode mixing and transition between different damping regimes.

Contribution

It uncovers a cascade of exceptional points in Kerr black hole quasinormal modes, demonstrating adiabatic ergodicity and new spectral phenomena.

Findings

Infinite sequence of exceptional points near extremality

Transition between damped and zero-damping modes

Geometric phase enables adiabatic mode mixing

Abstract

We uncover a cascade of exceptional points (EPs) in the quasinormal mode spectrum of massive scalar perturbations of Kerr black holes, revealing an intricate non-Hermitian structure underlying their linear response. The cascade originates from a single damped mode that enters the extremal spectrum for sufficiently large field masses. We obtain evidence for an infinite sequence of EPs in the $(\ell,m)=(1,1)$ and $(2,2)$ sectors near the extremal limit, mediating the transition between damped and zero-damping modes. Each EP carries a geometric phase that enables adiabatic mode mixing across the entire overtone spectrum, a phenomenon we refer to as adiabatic ergodicity.