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

Abstract

Extended gravitational decoupling can add hair to the black holes in general relativity by adding extra sources. The quasinormal modes of hairy black holes caused by gravitational decoupling for the massless scalar field, electromagnetic field, and axial gravitational perturbation are investigated. The equation of effective potential for three perturbations is derived in hairy black holes 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. Particularly, we find that the response of hairy black hole spacetime to axial gravitational perturbations is completely different from scalar field and electromagnetic field perturbations, which may be due to the fact that the gravitational radiation produced by the perturbations of the hairy black hole metric itself is much stronger than that of the external field. Furthermore, we have calculated the bounds on this greybody factor and high-energy absorption cross section with the Sinc approximation. The study reveals that the charges ($\alpha$ and $l_0$) generating primary hair contributes positively to the greybody bounds and absorption cross section, whereas the tidal charge $Q$ from the extra sources does the opposite