  The geometry of a spacetime containing a wormhole generated by a spherically
symmetric electric field is investigated in detail. These solutions arise in
high-energy extensions of General Relativity formulated within the Palatini
approach and coupled to Maxwell electrodynamics. Even though curvature
divergences generically arise at the wormhole throat, we find that these
spacetimes are geodesically complete. This provides an explicit example where
curvature divergences do not imply spacetime singularities.
