Plasma magnetosphere of deformed magnetized neutron star

The plasma magnetosphere surrounding a rotating magnetized neutron star described by non-Kerr spacetime metric in slow rotation approximation has been studied. First we have studied the vacuum solutions of the Maxwell equations in spacetime of slowly rotating magnetized non-Kerr star with dipolar magnetic configuration. Then for the magnetospheric model we have derived second-order differential equation for electrostatic potential from the system of Maxwell equations in spacetime of slowly rotating magnetized non-Kerr star. Analytical solutions of Goldreich-Julian (GJ) charge density along open field lines of slowly rotating magnetized non-Kerr neutron star have been obtained which indicate the modification of an accelerating electric field, charge density along the open field lines and radiating losses of energy of the neutron star by the deformation parameter.