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

Non-Twisting and Twisting Solutions of the Einstein Field Equations of a Skyrmionic String