We study static magnetic monopoles in the context of varying-$\alpha$ theories and show that there is a group of models for which the ’t Hooft-Polyakov solution is still valid. Nevertheless, in general static magnetic monopole solutions in varying-$\alpha$ theories depart from the classical ’t Hooft-Polyakov solution with the electromagnetic energy concentrated inside the core seeding spatial variations of the fine-structure constant. We show that Equivalence Principle constraints impose tight limits on the allowed variations of $\alpha$ induced by magnetic monopoles which confirms the difficulty to generate significant spatial variation of the fine-structure constant found in previous works. This is true even in the most favorable case where magnetic monopoles are the source for these variations.

• Received 15 July 2005

DOI:https://doi.org/10.1103/PhysRevD.72.103504