Dynamics of test particles and scalar perturbation around an Ayón–Beato–García black hole coupled with a cloud of strings

In this paper, we examine the geodesic motion and scalar perturbations of the Ayón–Beato–García black hole coupled with a cloud of strings, using the effective potential approach to analyze the trajectories of massless and massive test particles. The combined effects of nonlinear electrodynamics and the cloud of strings significantly modify the spacetime geometry, leading to distinct dynamical properties for test particles, including the stability and escape conditions of null and time-like geodesics. We also study scalar perturbations by deriving the Klein–Gordon equation for massless scalar fields in this spacetime, revealing an effective potential that depends on the parameters of nonlinear electrodynamics and the cloud of strings. Additionally, we compute the greybody factors to explore the energy transmission and absorption properties of the black hole, showing that both the nonlinear electrodynamics and the cloud of strings play a pivotal role in modulating these factors, thereby influencing the energy spectrum of scalar radiation.