Gravitational stability of local strings

The full coupled gravity-string field equations are considered and they are used to show that a general local string will have an asymptotically conical structure. For the case of the Abelian Higgs model with U(1) gauge invariance, the gravitational field of a simple local string to first order in G${\mathrm{\eta }}^2$ is exhibited. Then a C-energy argument is used to suggest stability at this linearized level.