  We explore the structure of a dipole-type vacuum field of a slowly rotating
magnetic star near the horizon of a supermassive black hole, where the
structure of field lines becomes highly distorted by effects of strong gravity.
Such a situation may occur near a neutron star in the final stages of a
plunging trajectory into a galactic center. We solve Maxwell's equations in the
Rindler approximation for the rotating conducting source of dipolar magnetic
field arbitrarily inclined with respect to the axis of rotation. For the fixed
inclination angle we calculate the field including the radiative terms while in
the general case we discuss the electromagnetic field considering the
near-field terms only. In the latter case we investigate the emergence of
magnetic null points within the vacuum magnetosphere. Null points become highly
relevant in the presence of astrophysical plasma where they are connected with
processes of magnetic reconnection and mass ejection.
