Regular solution of 't Hooft's magnetic monopole model in curved space

Abstract

A regular solution of 't Hooft's magnetic monopole model in curved space is presented. As in flat space, an analytical solution seems impossible, but by using the Einstein equations to eliminate the gravitational degrees of freedom, a positive-definite energy functional is constructed, which at its minimum gives both the required solution and the energy of the system. To first order in the gravitational constant $G$, the energy can be expressed in terms of the flat-space solutions only, whereas for general $G$ a positive lower bound is derived.