Dynamics of massless scalar field perturbations and the geodesic structure around a non-minimal Einstein–Yang–Mills black holes

This study undertakes a detailed analysis of geodesic motion, tidal forces and massless scalar field perturbations in the geometry of non-minimal Einstein–Yang–Mills black holes. Particular attention is devoted to the role of the black hole mass M , charge Q and the non-minimal coupling parameter ξ in governing the propagation characteristics of scalar waves as well as the trajectories of test particles. First, we derive the effective potential for massless scalar fields in the geometry of non-minimal Einstein–Yang–Mills black holes, revealing how increasing the charge Q provides a stronger potential barrier, lessening the transmission probability for low-energy waves. Simultaneously, large values of ξ which lead to stronger coupling between the spacetime curvature and Yang–Mills field enhance the potential barrier, suppressing wave transmission and enhancing the reflective properties of the black hole. These behaviors significantly affect the greybody factor, which measures the probability of scalar wave transmission across the potential barrier. We find that higher charge consistently increases the greybody factor, while stronger coupling ξ suppresses it, particularly in the low-frequency regime, thus decreasing the black hole’s transparency to scalar waves. Additionally, we conduct a detailed analysis of geodesic deviation vectors in the black hole spacetime revealing how tidal forces induced by spacetime curvature alter the relative motion of neighboring test particles. The results demonstrate that the non-minimal coupling significantly modifies both the greybody spectrum and the tidal behavior of freely falling particles through its influence on the effective potential and spacetime geometry. By establishing a direct connection between wave scattering and geodesic dynamics, the present study offers new insight into the physical consequences of non-minimally coupled Yang–Mills fields and provides a useful framework for future investigations of black hole perturbations and modified gravity.