Quasinormal Modes and Greybody Factors of Charged Symmergent Black Hole

Abstract: In this paper, we investigate quasinormal modes (QNMs) and greybody factors within the framework of Symmergent gravity, an emergent gravity model with an $R + R^2$ curvature sector. Building on our previous work on static spherically-symmetric solutions [Class. Quant. Grav. 40 (2023) 19, 195003], we explore the effects of the key parameters, including the quadratic curvature coupling parameter $c_{\rm O}$ and the vacuum energy parameter $\alpha$. For both scalar and electromagnetic perturbations, an increase in $\alpha$ leads to a nearly linear rise in both oscillation frequencies and damping rates. The other parameter $c_{\rm O}$ affects the QNMs spectrum nonlinearly. Additionally, the charge $Q$ of the black hole introduces nonlinear behavior, where higher charges amplify the black hole's electromagnetic field, resulting in increased oscillation frequencies and faster stabilization. These findings enhance our understanding of charged black hole stability and gravitational wave astrophysics. Further, the analysis of greybody factors reveals that increasing $\alpha$, $c_{\rm O}$, and $Q$ reduces the absorption of radiation, with electromagnetic perturbations reaching maximum absorption at slightly lower frequencies compared to scalar perturbations.