COMPLETE MODEL OF A SELF-GRAVITATING COSMIC-STRING - A NEW CLASS OF EXACT-SOLUTIONS

We find solutions of Einstein's field equation for topologically stable strings associated with the breaking of a U(1) symmetry. Strings form in many GUT's and are expected whenever the homotopy group II1(M(0)) is nontrivial. The behavior of the fields making up the string is described by the Euler-Lagrange equations. These fields appear in the energy-momentum tensor so we must solve simultaneously for the coupled Einstein-scalar-gauge field equations. Numerical results are obtained using a Taylor-series method. We obtain a five-parameter family of solutions and discuss the assumption of regularity at the origin. Finally, we introduce the idea of gravitational lensing near the center of the string as a possible physical effect.