  We consider a self-gravitating string generated by a global vortex solution
in general relativity. We investigate the Einstein and field equations of a
global vortex in the region of its central line and at a distance from the
centre of the order of the inverse of its Higgs boson mass. By combining the
two we establish by a limiting process of large Higgs mass the dynamics of a
self-gravitating global string. Under our assumptions the presence of
gravitation restricts the world sheet of the global string to be totally
geodesic.
