  An important issue in the asteroseismology of compact and magnetized stars is
the determination of the dissipation mechanism which is most efficient in
damping the oscillations when these are produced. In a linear regime and for
low-multipolarity modes these mechanisms are confined to either
gravitational-wave or electromagnetic losses. We here consider the latter and
compute the energy losses in the form of Poynting fluxes, Joule heating and
Ohmic dissipation in a relativistic oscillating spherical star with a dipolar
magnetic field in vacuum. While this approach is not particularly realistic for
rapidly rotating stars, it has the advantage that it is fully analytic and that
it provides expressions for the electric and magnetic fields produced by the
most common modes of oscillation both in the vicinity of the star and far away
from it. In this way we revisit and extend to a relativistic context the
classical estimates of McDermott et al. Overall, we find that
general-relativistic corrections lead to electromagnetic damping time-scales
that are at least one order of magnitude smaller than in Newtonian gravity.
Furthermore, with the only exception of $g$ (gravity) modes, we find that $f$
(fundamental), $p$ (pressure), $i$ (interface) and $s$ (shear) modes are
suppressed more efficiently by gravitational losses than by electromagnetic
ones.
