  We revisit particle acceleration in the polar cap region of a neutron star by
taking into account both general relativistic effects and the presence of
toroidal oscillations at the star surface. In particular, we address the
question of whether toroidal oscillations at the stellar surface can affect the
acceleration properties in the polar cap. We solve numerically the relativistic
electrodynamics equations in the stationary regime, focusing on the computation
of the Lorentz factor of a space-charge-limited electron flow accelerated in
the polar cap region of a rotating and oscillating pulsar. To this extent, we
adopt the correct expression of the general relativistic Goldreich-Julian
charge density in the presence of toroidal oscillations. Depending on the ratio
of the actual charge density of the pulsar magnetosphere to the
Goldreich-Julian charge density, we distinguish two different regimes of the
Lorentz factor of the particle flow, namely an oscillatory regime produced for
sub-GJ current density configurations, which does not produce an efficient
acceleration, and a true accelerating regime for super-GJ current density
configurations. We find that star oscillations may be responsible for a
significant asymmetry in the pulse profile that depends on the orientation of
the oscillations with respect to the pulsar magnetic field. In particular,
significant enhancements of the Lorentz factor are produced by stellar
oscillations in the super-GJ current density regime.
