Avoided crossings and resonances in black hole ringdown with coupled fields: A case study of the Einstein-Maxwell-axion system

Abstract

Avoided crossings in black hole quasinormal-mode (QNM) spectra exhibit characteristic resonant properties, including enhanced excitation factors. We extend the study of this phenomenon to perturbation systems with multiple coupled fields and investigate its consequences for ringdown waveforms. As a concrete example, we consider a charged black hole in the Einstein-Maxwell-axion system, whose QNM branches can be classified according to the gravitational, electromagnetic, and axion modes to which they continuously connect in the decoupling limit. We focus on an avoided crossing between the gravity- and electromagnetic-led branches thus defined. We verify that the QNM reconstruction accurately reproduces the ringdown portion of the directly evolved time-domain waveform. Near the avoided crossing, an effectively slower decay emerges for particular initial perturbations, while the resonantly enhanced contributions from the two QNMs largely cancel in the physical waveform. The QNM decomposition further reveals an exchange of the physical characters of the two branches across the resonance. These results characterize the imprint of resonances on black hole ringdown in systems with multiple coupled fields.