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

Particle acceleration in the polar cap region of an oscillating neutron star