Effect of the cosmological constant on the deflection angle by a rotating cosmic string

TL;DR

This paper investigates how the cosmological constant influences the light deflection angle caused by a rotating cosmic string with internal structure, using geodesic equations and the Gauss-Bonnet theorem, resolving previous inconsistencies.

Contribution

It generalizes the deflection angle calculation for rotating cosmic strings by including the cosmological constant and internal energy density, and resolves prior methodological inconsistencies.

Findings

The cosmological constant significantly affects the deflection angle.

The rotation of the cosmic string does not influence the deflection angle.

The methods of geodesic equations and Gauss-Bonnet theorem agree when higher order terms are included.

Abstract

We report the effect of the cosmological constant and the internal energy density of a cosmic string on the deflection angle of light in the spacetime of a rotating cosmic string with internal structure. We first revisit the deflection angle by a rotating cosmic string and then provide a generalization using the geodesic equations and the Gauss-Bonnet Theorem. We show there is an agreement between the two methods when employing higher order terms of the linear mass density of the cosmic string. By modifying the integration domain for the global conical topology, we resolve the inconsistency between these two methods previously reported in the literature. We show that the deflection angle is not affected by the rotation of the cosmic string; however, the cosmological constant $\Lambda$ strongly affects the deflection angle, which generalizes the well-known result.