Exceptional Points and Resonance in Black Hole Ringdown

TL;DR

This paper introduces an exceptional-point framework for black-hole ringdown analysis that captures resonance effects beyond traditional quasinormal modes, revealing enhanced mode contributions and a new observable in the near-EP regime.

Contribution

It develops a first-principles exceptional-point approach to characterize black-hole resonances, surpassing standard quasinormal-mode analysis.

Findings

Resonance produces enhanced mode contributions in the time domain.

The EP frequency, as the average of resonant modes, is a key observable.

The framework captures avoided crossing effects near exceptional points.

Abstract

We propose an exceptional-point (EP) framework for black-hole ringdown beyond the standard quasinormal-mode (QNM) paradigm. It provides a first-principles characterization of the resonance associated with avoided crossings near EPs, an effect that conventional QNM analysis cannot fully capture. Employing a phenomenological environmental black-hole model with the hyperboloidal framework, we identify near-coalescence of both QNM eigenvalues and eigenfunctions, and directly demonstrate that the resonance produces enhanced mode contributions in the time domain, resulting in characteristic departures from exponentially damped oscillations. Our formulation further reveals that the EP frequency, given by the average of the resonant modes, emerges as the physically relevant observable in the near-EP regime, and offers a robust foundation for modeling and extracting resonant ringdown signals.