  We investigate the electromagnetic fields in the vacuum exterior of a
rotating relativistic star endowed with a magnetic dipole moment, and with the
stellar surface behaving as a perfect conductor. While the stellar rotation is
treated in the slow-approximation of general relativity, we do not restrict our
attention to slowly rotating electromagnetic fields, and take our analysis
beyond the low-frequency approximation considered so far. When the dipole
moment is misaligned with the rotational axis, our approach does not yield
analytic solutions as in Rezzolla et al. (2001a, b), but determines the
properties of the electromagnetic fields approximately and semi-analytically,
by computing the coefficients of simple expressions for the fields through the
numerical solution of two partial differential equations. Because our approach
provides a solution which is in principle valid throughout space, we can
evaluate the accuracy and/or invalidity of previously known analytic
expressions at different distances from the stellar surface. Overall, the
solutions found in this way represent an efficient way of bridging in a single
semi-analytic formalism the strongly relativistic (Rezzolla et al. 2001a, b)
and the asymptotic regimes (Deutsch 1955) for which analytic solutions have
been found.
