The magnetosphere of an oscillating neutron star. Non-vacuum treatment

We generalize a formula for the Goldreich-Julian charge density (\\rho), originally derived for rotating neutron star, for arbitrary oscillations of a neutron star with arbitrary magnetic field configuration under assumption of low current density in the inner parts of the magnetosphere. As an application we consider toroidal oscillation of a neutron star with dipole magnetic field and calculate energy losses. For some oscillation modes the longitudinal electric field can not be canceled by putting charged particles in the magnetosphere without a presence of strong electric current j = (c/(ømega r)) the magnetosphere, and cannot be described by vacuum formulas.

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