  Neutron stars and black holes are the most compact astrophysical objects we
can think of and as a consequence they are the main sources of gravitational
waves. There are many astrophysically relevant scenarios in which these objects
are immersed in or endowed with strong magnetic fields, in such a way that
gravitational perturbations can couple to electromagnetic ones and can
potentially trigger synergistic electromagnetic signatures. In a recent paper
we derived the main equations for gravito-electromagnetic perturbations and
studied in detail the case of polar electromagnetic perturbations driven by
axial gravitational perturbations. In this paper we deal with the case of axial
electromagnetic perturbations driven by polar black-hole or neutron stars
oscillations, in which the energy emitted in case is considerably larger than
in the previous case. In the case of neutron stars the phenomenon lasts
considerably longer since the fluid acts as an energy reservoir that shakes the
magnetic field for a timescale of the order of secs.
