# Effect of Lorentz Symmetry Breaking on the Deflection of Light in a Cosmic String Spacetime

## TL;DR

This paper studies how Lorentz symmetry breaking influences light deflection around cosmic strings, revealing significant modifications in the deflection angle due to LSBE parameters, especially in rotating scenarios, with some cases unaffected.

## Contribution

It introduces a detailed analysis of Lorentz symmetry breaking effects on light deflection in cosmic string spacetimes, including rotating cases and different vector fixings, using the Gauss-Bonnet theorem.

## Key findings

- LSBE causes significant modifications in deflection angles.
- First and second order correction terms depend on LSBE and cosmic string parameters.
- Deflection angle is unaffected by LSBE in fixed time-like vector cases.

## Abstract

We investigate the Lorentz symmetry breaking effects (LSBE) on the deflection of light by a rotating cosmic string spacetime in the weak limit approximation. We first calculate the deflection angle by a static cosmic string for a fixed spacelike 4-vector case (FSL) with the corresponding effective-string optical metric using the Gauss-Bonnet theorem (GBT). Then, we focus on a more general scenario, namely we calculate the deflection angle by a rotating cosmic string applying the GBT to Randers effective-string metric. We obtain a significant modification in the deflection angle because of the LSBE parameter. We find a first and second order correction terms due to the global effective topology which are proportional to the cosmic string and LSBE parameter, respectively. Finally, for a fixed time-like 4-vector (FTL) case, we show that the deflection angle is not affetced by LSBE parameter.