  Magnetic fields interact with gravitational waves in various ways. We
consider the coupling between the Weyl and the Maxwell fields in cosmology and
study the effects of the former on the latter. The approach is fully analytical
and the results are gauge-invariant. We show that the nature and the outcome of
the gravito-magnetic interaction depends on the electric properties of the
cosmic medium. When the conductivity is high, gravitational waves reduce the
standard (adiabatic) decay rate of the B-field, leading to its superadiabatic
amplification. In poorly conductive environments, on the other hand,
Weyl-curvature distortions can result into the resonant amplification of
large-scale cosmological magnetic fields. Driven by the gravitational waves,
these B-fields oscillate with an amplitude that is found to diverge when the
wavelengths of the two sources coincide. We present technical and physical
aspects of the gravito-magnetic interaction and discuss its potential
implications.
