  We consider a magnetic flux pointing in the $z$ direction of an axially
symmetric space-time (Melvin Universe) in a Born-Infeld-type extension of
General Relativity (GR) formulated in the Palatini approach. Large magnetic
fields could have been produced in the early Universe, and given rise to
interesting phenomenology regarding wormholes and black hole remnants. We find
a formal analytic solution to this problem that recovers the GR result in the
appropriate limits. Our results set the basis for further extensions that could
allow the embedding of pairs of black hole remnants in geometries with intense
magnetic fields.
