Echoes of a hairy black hole from gravitational decoupling

Le résumé fourni par la source

Abstract We study axial gravitational perturbations of a hairy black hole constructed in the framework of gravitational decoupling and investigate the geometric origin of echo-like late-time signals in this spacetime. We derive the odd-parity master equation and the corresponding effective potential, and compute the quasinormal mode spectrum by using frequency-domain and time-domain methods. We show that the axial potential develops a double-peak structure that supports a trapping cavity and gives rise to echo-like waveforms. The representative double-peak configurations also exhibit an unstable--stable--unstable light-ring structure, which provides the null-geodesic counterpart of the trapping cavity in the eikonal limit. Therefore, the echoes are not produced by an artificially imposed near-horizon condition, but emerge dynamically from the geometric structure of the effective potential. Our results provide a useful framework for probing black hole hair through gravitational-wave ringdown and for exploring possible observational departures from the standard no-hair paradigm.

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