Weak field deflection angle by regular black holes with cosmic strings using the Gauss-Bonnet theorem

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 a regular black hole with cosmic strings. We discuss that increasing cosmic string parameter μ and mass M0 will increase the bending angle.