Lensing effect of a cosmic string in Chern-Simons gravity

TL;DR

This paper explores how conformally transformed flat space-time metrics in Chern-Simons gravity can produce lensing effects similar to cosmic strings, revealing new solutions and light-ray behaviors.

Contribution

It demonstrates that conformal transformations solve Witten's equation in Chern-Simons gravity and produce cosmic string lensing effects, including novel light-ray circular paths.

Findings

Conformal transformations of flat metrics solve Witten's equation.

Such solutions can model cosmic string lensing effects.

Light rays can follow open circular paths near the string.

Abstract

It is pointed out that any conformally transformed of a flat space-time metric $\ball g_{ij} = f(x)\;\eta_{ij}$ is a solution to Witten's equation of Chern-Simons gravity, which holds outside matter in (2+1) dimensions. It is also shown that a simultaneous exterior solution to both Witten's and Einstein's equations, yields the lensing effect of an isolated cosmic string, if $f(x)$ is reduced to an arbitrary dimensionless constant. However, the solution to Witten's equation with $f(x)$ being an arbitrary and continuous function of space-time coordinates, also leads to an open circular path for a light ray near the string.