Vortex Solution of the Gravitational Field Equation of a Twisted Skyrme Strings

We construct non-linear sigma model plus Skyrme term (Skyrme model) with a twist in the gravitational field. To simplify the solution, first we examine non-linear sigma model without Skyrme term, in particular with a twist, which comprises a vortex solution with an added dependence on a twist term $mkz$, where $z$ is the vertical coordinate. We find that vortex solution for non-linear sigma model with a twist is similar with vortex solution without a twist. The work is still progress.