Quasinormal Modes and Grey-Body Factors of Scalar, Electromagnetic and Dirac Fields Around Einasto-Supported Regular Black Holes

Abstract: We study quasinormal modes and grey-body factors of scalar, electromagnetic and Dirac test fields for a black hole surrounded by matter distributed according to the Einasto density profile. The quasinormal spectrum is calculated using the high-order WKB method with Padé approximants and checked by the time-domain integration. For small values of the Einasto index $\tilde n=1/2$ and $\tilde n=1$, the fundamental modes remain close to their Schwarzschild values, while for $\tilde n=5$ the oscillation frequency increases and the damping rate decreases as the halo parameter grows. Grey-body factors are much less sensitive to the halo environment: the main effect is a mild suppression at low frequencies caused by a moderate increase of the effective potential near the horizon. At higher frequencies the transmission probabilities remain close to the Schwarzschild case.