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

TL;DR

This paper investigates how massless Dirac perturbations and weak gravitational lensing are affected by a static black hole in f(Q) gravity, revealing stability and the influence of nonmetricity on quasinormal modes and deflection angles.

Contribution

It introduces the analysis of massless Dirac perturbations and weak deflection angles in f(Q) gravity, highlighting the effects of the nonmetricity parameter on black hole stability and gravitational lensing.

Findings

Black hole remains stable against Dirac perturbations.

Increasing nonmetricity parameter decreases oscillatory frequency.

Nonmetricity parameter reduces the 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.