The Gravitational Field of a Twisted Skyrmion String

TL;DR

This paper investigates the gravitational effects of a twisted Skyrmion string, a topological defect modeled by a nonlinear sigma model with a twist term, using Einstein's equations in a static, cylindrically symmetric spacetime.

Contribution

It introduces a model for the gravitational field of a twisted Skyrmion string, incorporating a twist term to stabilize the vortex solution within a general relativistic framework.

Findings

Derived Einstein equations for the twisted Skyrmion string

Modeling of the gravitational field in a static cylindrically symmetric spacetime

Work is ongoing to solve the equations and analyze the solutions

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 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.