Pulsars are believed to loose their rotational kinetic energy primarily by alarge amplitude low frequency electromagnetic wave which is eventuallyconverted into particle creation, acceleration and followed by a broad bandradiation spectrum. To date, there exist no detailed calculation of the exactspin-down luminosity with respect to the neutron star magnetic moment and spinfrequency, including general-relativistic effects. Estimates are usually givenaccording to the flat spacetime magnetodipole formula. The present paper pursueour effort to look for accurate solutions of the general-relativisticelectromagnetic field around a slowly rotating magnetized neutron star. In aprevious work, we already found approximate stationary solutions to thisproblem. Here we address again this problem but using a more general approach.We indeed solve the full set of time-dependent Maxwell equations in a curvedvacuum space-time following the 3+1 formalism. The numerical code is based onour pseudo-spectral method exposed in a previous paper for flat space-time. Weadapted it to an arbitrary fixed background metric. Stationary solutions arereadily obtained and compared to semi-analytical calculations.
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