Researchers have studied the gravitational perturbations of black holes endowed with a particular type of primary scalar 'hair', within the framework of shift-symmetric beyond-Horndeski gravity. The aim is to understand how these exotic features affect the response of black holes to perturbations, a crucial aspect for gravitational wave detection and the validation of theoretical models.

The study focused on the axial sector of the perturbations. Time-domain evolutions were performed using both the physical metric and an effective metric, allowing for the quantification of differences in the response characteristics of solutions with varying scalar 'hair' properties. In the frequency domain, the quasinormal mode (QNM) spectrum was explored using the physical-metric formulation, which verified and extended previous approximate calculations based on the effective metric. Furthermore, the corresponding greybody factors and absorption cross-sections were computed.

Quasinormal modes are the 'voices' of black holes, the frequencies at which they vibrate after being perturbed, and their study is fundamental for gravitational wave astrophysics. Greybody factors, on the other hand, describe the probability of waves being absorbed or reflected by the black hole. The work also used localized deformations of the effective potential as a diagnostic tool to assess the relative stability of the observed quasinormal frequencies and greybody factors. These results are important for refining black hole models and for the interpretation of future astrophysical observations.