Gravity of Global U(1) Cosmic String

We show that a static one-dimensional U(1) global string is confined by its own gravitational field to a finite radius. The energy-momentum tensor of a global string decreases exponentially with the distance from its core. We call it self-localization. We show that the order parameter is a decreasing function of the symmetry breaking energy scale. We have found the maximum value of the energy scale _max, where the order parameter vanishes. Beyond the maximum value > _max the gravitational field of a global string gets so strong, that it restores the initial unbroken symmetry. In the close vicinity of the maximum value _max of the symmetry breaking scale we get a closed-form solution for the metric. It reduces to the Galileo metric on the axis and transforms into the Kasner-type solution near the boundary of a string.