  We construct non-linear sigma model plus Skyrme term (Skyrme model) with a
twist in the gravitational field. We try to solve the Einstein field equations
for small and large values of $r$, with and without twist. We prove that no
non-twisting or twisting solutions extending from $r=0$ to $r=\infty$ exist. At
last, we try to solve non-twisting and twisting solutions of the Einstein field
equations with a finite radius. We find that there are no solutions with a
finite radius that can satisfy the junction conditions at the boundary radius
$r=r_b$, where $r_b$ is a finite radius.
