Quasinormal Modes and Greybody Factors of Scalar Field Perturbations in the NED Corrected Charged Black Hole Spacetime

Abstract: Inspired by the quark-antiquark confinement potential, Mazharimousavi et al. \cite{Mazharimousavi:2023okd} proposed a nonlinear electrodynamics (NED) model, and based on this model, they constructed a charged black hole solution that includes a logarithmic correction term ($\propto \frac{\zeta \ln r}{r}$). On the basis of the Reissner-Nordstr\"om metric, this solution realizes a long-range confinement correction by introducing the NED parameter $\zeta$, providing a new theoretical perspective for explaining the anomalies in galaxy rotation curves. To deeply explore the dynamic properties of this black hole solution, this paper combines two complementary methods, namely, time-domain evolution and the WKB approximation, to calculate the quasinormal mode (QNM) spectrum of its scalar field perturbations. The research results show that the oscillation frequencies and decay rates of the low-order QNM modes decrease monotonically with the increase of the NED parameter $\zeta$, and exhibit an approximately linear dependence. The analysis of the greybody factor (GF) indicates that as $\zeta$ increases, the transmittance of the low-frequency scalar field also increases. The enhanced long-range confinement effect caused by the increase of $\zeta$ makes low-frequency perturbations more likely to survive and propagate in space-time on the one hand, and at the same time enhances the transmission ability of the low-frequency scalar field. These characteristics provide key theoretical predictions and potential observational features for testing and constraining such NED models in a strong gravitational field environment in the future using the observational data of gravitational wave astronomy or Hawking radiation.