Particle motion and lensing with plasma of black hole in coincident \(f\left( \mathbb{Q}, \mathbb{B}_Q\right) \) gravity coupled to nonlinear electrodynamics

Abstract

This research is motivated by a study that investigates the features of black hole (BH) under coincident \(f\left( \mathbb {Q}, \mathbb {B}_Q\right) \) gravity coupled with nonlinear electrodynamics. The study also explores BH shadows and weak gravitational plasma lensing. We examine the effective potential, or ISCO, for the motion of large particles and photons to analyze particle dynamics. To examine the gravitational lensed photons, we suppose the weak gravitational field. Here we consider three plasma domains to fulfill this lensing objective: a non-singular isothermal sphere, a singular isothermal sphere, and uniform plasma. Furthermore, we examine the Gibbons-Werner methodology for calculating the deflection angle of light caused by the BH in a scenario with the weak gravitational field. This illustrates that bending light is a topological and global phenomenon. To accomplish this, we employ the Gauss–Bonnet theorem (GBT) and deduce the Gaussian curvature. Moreover, we calculate the deflection angle at which a plasma medium deflects light. The graphical behavior of BH in vacuum and plasma mediums is also investigated.