Toward the quasi-steady state electrodynamics of a neutron star

We consider the electrodynamics of a rotating magnetized neutron star with allowance for the quasisteady state regime of charged particle ejection from the polar cap into the inner magnetosphere. We derive basic equations within the framework of a general relativistic formalism and present the analytic solutions. We demonstrate that the quasi-steady state supply of electrons into the region of open field lines reduces the total power put into the acceleration of primary particles, although the total power corresponding to a steady state solution in general relativity is increased compared to the hat-space solution. Also, we illustrate that temporarily modulated ejection of electrons from the stellar surface results in substantial modulation of an accelerating electric field and charge density along the open field lines. We briefly outline the implications of this effect for the pulsars.