Analyzing the gravitational lensing and epicyclic oscillations around a regular charged black hole

The paper provides an analysis of gravitational weak lensing, Einstein rings, and fundamental frequencies within the context of the regular charged black hole. In this paper we deal with two regular charged black hole geometries. We calculate the deflection angle of light by the charged black hole solutions under weak field conditions. This indicates that the bending of light is a global and topological phenomenon. To achieve this, we derive the Gaussian curvature and apply the Gauss–Bonnet theorem. Additionally, we calculate the deflection angle at which light becomes distorted by a plasma medium for both charged black hole cases. We also examine the graphical behavior of black holes in both non-plasma and plasma mediums. Furthermore, we investigate the fundamental frequencies using three distinct models of a charged black hole. Lastly we compute the Einstein ring for the regular charged black hole.