Echoes of the gravitational decoupling: scalar perturbations and quasinormal modes of hairy black holes

The behavior of hairy black hole solutions, obtained by the gravitational decoupling (GD) method, is investigated under scalar perturbations. The quasinormal mode frequencies of such solutions are regulated by GD hair. The numerically generated wave solutions are derived for a range of values for the GD hairy black hole parameters, with higher-frequency modes very sensitive to them. The results are confronted with the corresponding ones for the Schwarzschild solution, whose deviations from it demonstrate a unique physical identification of GD hairy black holes. The method here presented comprises the first steps toward the obtainment of the observable signature of GD hairy black holes at ground-based detectors, emitted from coalescing binary systems of GD hairy black hole mergers in the ringdown phase.