Massless Dirac Perturbations of black holes in f(Q) gravity: quasinormal modes and weak deflection angle

Abstract: This article considers a static and spherical black hole (BH) in f(Q) gravity. f(Q) gravity is the extension of symmetric teleparallel general relativity, where both curvature and torsion are vanishing, and gravity is described by nonmetricity. In this study, we investigate the possible implications of quasinormal modes (QNM) modified Hawking spectra, and deflection angles generated by the model. The WKB method is used to solve the equations of motion for massless Dirac perturbation fields and explore the impact of the nonmetricity parameter ($Q_{0}$). Based on the QNMs computation, we can ensure that the BH is stable against massless Dirac perturbations and as $Q_{0}$ increases the the oscillatory frequency of the mode decrease. We then discuss the weak deflection angle in the weak field limit approximation. We compute the deflection angle up to the fourth order of approximation and show how the nonmetricity parameter affects it. We find that the $Q_{0}$ parameter reduces the deflection angle.