  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.
