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

Gravitational decoupling can add hair to the black holes by adding extra sources. The quasinormal modes of hairy hole caused gravitational for massless scalar field, electromagnetic and perturbation are investigated. equations effective potential three perturbations derived in spacetime. We also study time evolution corresponding perturbations, mode frequencies calculated using Prony method through time-domain profiles. By analyzing influence hairs ($\alpha$, $l_0$ $Q$) we studying on mode, find that $\alpha$ decrease oscillation frequency wave signal, $Q$ increase its frequency.Furthermore, have bounds greybody factor high-energy absorption cross section with Sinc approximation, which reveals presence charges ($\alpha$ $l_0$) generating primary probability radiation arriving spatial infinity, whereas charge from sources does opposite.