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 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 (alpha, l0 and Q) for the black holes we are studying on quasinormal modes, we find that the hairs alpha and l0 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 (alpha and l0) 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.

Automated summary

Gravitational decoupling can add hair to black holes, and we investigated the quasinormal modes of hairy black holes caused by gravitational decoupling. We derived the equations of effective potential for three perturbations in a hairy black hole spacetime and studied their time evolution. By analyzing the influence of the hairs (alpha, l0, and Q) on quasinormal modes, we found that alpha and l0 decrease the oscillation frequency of gravitational-wave signal, while Q increases it. Additionally, we calculated the bounds of the greybody factor and high-energy absorption cross section, showing that primary hair generated by charges (alpha and l0) can increase the probability of gravitational radiation reaching spatial infinity, while the charge Q from extra sources has the opposite effect.