Null Geodesics in the Reissner-Nordström Black Hole Spacetime Pierced by a Cosmic String

Abstract

In this paper, we investigate null geodesics in the spacetime of a Reissner-Nordström black hole pierced by a cosmic string. Analysis of the equations of motion reveals that null geodesics in this conical spacetime can be classified into three main categories, with the classification entirely determined by the ratio $|Q|/M$ (where $Q$ and $M$ denote the black hole charge and mass, respectively). Analytical solutions to the null geodesic equations are obtained for each category. Based on these solutions, we numerically simulate light trajectories and analyze in detail the effects of the black hole charge $Q$ and the cosmic string parameter $α$. It is found that the cosmic string parameter $α$ enhances the winding behavior of null geodesics across all three main categories. Finally, we consider light deflection in the equatorial plane and derive an expression for the deflection angle, revealing that the charge $Q$ decreases the deflection angle, whereas the cosmic string parameter $α$ increases it.