Quasi-normal modes and absorption section from regular black holes immersed in perfect fluid dark matter

We study scalar, electromagnetic and gravitational perturbations of three families of regular black holes, Hayward, Bardeen and Ayon–Beato–García immersed in a Perfect Fluid Dark Matter (PFDM) background. Using both the sixth-order WKB approximation and the Asymptotic Iteration Method (AIM), we determine the corresponding quasi-normal modes and absorption cross sections. By fixing the horizon radius, we analyze the dependence of the parameters of the black holes and the parameter of PFDM. The computed quasi-normal modes confirm the dynamical stability of the black holes under scalar, electromagnetic and gravitational perturbations. Furthermore, both the real and imaginary parts of the quasi-normal modes increase with the multipole number l, corresponding to higher oscillation frequencies and faster damping rates. On the other hand, absorption cross sections are compared under similar parametric conditions. The results demonstrate that PFDM influences the dynamical properties of regular black holes.