Mathematical modeling of the gravitational field of a twisted Skyrmion string

TL;DR

This paper develops a mathematical model for the gravitational field of a twisted Skyrmion string, incorporating a twist to stabilize vortex solutions within a cylindrically symmetric spacetime, extending nonlinear sigma models.

Contribution

It introduces a gravitational model for twisted Skyrmion strings by deriving Einstein equations with a cylindrically symmetric metric, including the twist for stabilization.

Findings

Derived Einstein equations for twisted Skyrmion strings.

Incorporated twist term to stabilize vortex solutions.

Model is in progress, extending nonlinear sigma models with gravity.

Abstract

In this paper we study the gravitational field of a straight string generated from a class of nonlinear sigma models, specifically the Skyrme model without a twist and the Skyrme model with a twist (the twisted Skyrmion string). The twist term, $mkz$, is included to stabilize the vortex solution. To model the effects of gravity, we replace the Minkowski tensor, $\eta^{\mu\nu}$, in the standard Skyrme Lagrangian density with a space-time metric tensor, $g^{\mu\nu}$, assumed to be static and cylindrically symmetric. The Einstein equations for the metric and field components are then derived. This work is still in progress.