How dark matter and quantum electrodynamics reshape black hole ringing

Quasinormal modes — the characteristic 'ringdown' frequencies of a perturbed black hole — are calculated for a charged black hole modified by two independent effects: Euler–Heisenberg nonlinear electrodynamics and a surrounding perfect-fluid dark matter distribution. Using two independent methods (asymptotic iteration and sixth-order WKB), the study maps out how the black hole charge, the nonlinear parameter, and the dark matter density each reshape the effective potential barrier seen by scalar and electromagnetic waves. The result is that both corrections shift oscillation frequencies and damping rates in distinct, separable ways, and also alter the greybody factors that govern how much radiation escapes to a distant observer.