# Weak gravitational lensing of regular black holes with cosmic strings using the Gauss-Bonnet theorem

## TL;DR

This paper studies how light bends around regular black holes with cosmic strings using the Gauss-Bonnet theorem, revealing the topological nature of gravitational lensing and effects of plasma media.

## Contribution

It applies the Gauss-Bonnet theorem to analyze light deflection in regular black holes with cosmic strings, incorporating plasma effects, which is a novel approach in this context.

## Key findings

- Light bending is a topological effect influenced by cosmic strings.
- Increasing cosmic string parameter and mass increases the deflection angle.
- Plasma medium affects the light deflection in the black hole spacetime.

## Abstract

In this paper, we investigate light bending in the spacetime of regular black holes with cosmic strings in weak field limits. To do so, we apply the Gauss-Bonnet theorem to the optical geometry of the black hole; and, using the Gibbons-Werner method, we obtain the deflection angle of light in the weak field limits which shows that the bending of light is a global and topological effect. Afterwards, we demonstrate the effect of a plasma medium on the deflection of light by RBCS. We discuss that increasing cosmic string parameter $\mu$ and mass $M_0$ will increase the bending angle.