We study a modified Yang-Mills-Higgs system coupled to Einstein gravity, with a direct coupling of the Higgs field to the scalar curvature. We are able to write a Bogomol'nyi type condition in curved space and show that the positive static energy functional is bounded. We then investigate non-Abelian spherically symmetric static solutions in a similar fashion to the 't Hooft-Polyakov monopole. After reviewing monopole solutions of this type, we also present dyon solutions.
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