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A pulsar is usually modeled as an oblique rotator with a magnetic dipole field.

An external observer sees a rotating magnetic field which induces an electric field which pulls plasma from the surface to the magnetosphere.

What is the origin of the plasma for an observer on the pulsar surface? He sees a static (?) magnetic field, how can he explain the presence of the plasma in the magnetosphere?

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OK, I have asked around and it seems I have solved this paradox.

The main point is that the observer on the pulsar is not inertial, this causes the appearance of two terms in Maxwell's equations: an apparent charge density and an apparent current density that must be compensated for.

The full solution of the paradox is in this old paper by Schiff, in which he tackles a similar paradox ideated by Oppenheimer.

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