  In this work the possible geodesic completeness of an electromagnetic dipole
wormhole is studied in detail. The space-time contains a curvature singularity
and belongs to a class of solutions to the Einstein-Maxwell equations with a
coupled scalar field. Specifically, a numerical analysis is performed to
examine congruences of null geodesics that are directed toward the singularity.
The results found here show that, depending on the strength of the coupling
between the scalar and electromagnetic fields, the wormhole can be either
geodesically incomplete or complete. We then focus on those wormholes that are
geodesically complete and study the geometry of the neighborhood of their
singularity using Kaluza-Klein theory in a five-dimensional space-time. This
process allows us to provide a possible explanation of the completeness of
geodesics despite unbounded curvature.
