Аннотация:
Just as a rotating magnetised neutron star has material pulled away from its surface
to populate a magnetosphere, a similar process can occur as a result of neutron-
star pulsations rather than rotation. This is of interest in connection with the overall
study of neutron star oscillation modes but with a particular focus on the situation for
magnetars. Following a previous Newtonian analysis of the production of a force-free
magnetosphere in this way Timokhin et al. (2000), we present here a corresponding
general-relativistic analysis. We give a derivation of the general relativistic Maxwell
equations for small-amplitude arbitrary oscillations of a non-rotating neutron star
with a generic magnetic field and show that these can be solved analytically under the
assumption of low current density in the magnetosphere. We apply our formalism to
toroidal oscillations of a neutron star with a dipole magnetic field and find that the
low current density approximation is valid for at least half of the oscillation modes,
similarly to the Newtonian case. Using an improved formula for the determination of
the last closed field line, we calculate the energy losses resulting from toroidal stellar
oscillations for all of the modes for which the size of the polar cap is small.We find that
general relativistic effects lead to shrinking of the size of the polar cap and an increase
in the energy density of the outflowing plasma. These effects act in opposite directions
but the net result is that the energy loss from the neutron star is significantly smaller
than suggested by the Newtonian treatment
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