  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.
