EXISTENCE OF NON-TOPOLOGICAL MULTI-STRING SOLUTIONS FOR A GRAVITATIONAL O(3) GAUGE FIELD MODEL

Abstract

In this paper, we consider the self-dual equation arising from the Maxwell gauged O(3) model coupled with gravity. We prove the existence of non-topological multi-string solutions and obtain their decay estimates at infinity. Using the decay rates, we compute the static energy, the magnetic flux, and the total Gaussian curvature corresponding to our solutions. Our solutions are constructed by a perturbation argument with an application of the Implicit Function Theorem.