Probing hairy black holes caused by gravitational decoupling using quasinormal modes and greybody bounds

Abstract

Gravitational decoupling can add hair to the black holes by adding extra sources. The quasinormal modes of a hairy black hole caused by gravitational decoupling for the massless scalar field, electromagnetic field, and gravitational perturbation are investigated. The equations of the effective potential for three perturbations are derived in a hairy black hole spacetime. We also study the time evolution corresponding to the three perturbations, and the quasinormal mode frequencies are calculated using the Prony method through the time-domain profiles. By analyzing the influence of the hairs ($\ensuremath{\alpha}$, ${l}_{0}$ and $Q$) for the black holes we are studying on quasinormal modes, we find that the hairs $\ensuremath{\alpha}$ and ${l}_{0}$ decrease the oscillation frequency of the gravitational-wave signal, and the hair $Q$ increases its oscillation frequency. Furthermore, we calculate the bounds of the greybody factor and high-energy absorption cross section with the sinc approximation, which reveals that the presence of charges ($\ensuremath{\alpha}$ and ${l}_{0}$) generating primary hair can increase the probability of gravitational radiation arriving at spatial infinity, whereas the charge $Q$ from the extra sources does the opposite.