Solution for the relativistic magnetic field dynamics equation of neutron stars as magnetized, accreting, and rapidly rotating conductors in zero angular momentum observers (ZAMO) frame

Abstract

Solution for the relativistic magnetic field dynamics equation of neutron stars as magnetized conductors has been formulated by assuming the magnetic field as magnetized, rapidly rotating conductor, and accreting in Zero Angular Momentum Observers (ZAMO) frame. The magnetic field in a neutron star is assumed to be bipolar. The relativistic magnetic field dynamics equation of neutron stars as magnetized is obtained by formulating the contravariant tensor, the current density of four, and the relativistic second Maxwell equation. The form of the equation is the differential equation with the solution being the radial, polar, azimuth, and time functions. The equation obtained has the same pattern as a slow-rotating neutron star. But if it is assumed that the neutron star does not perform accretion, then the star's rotation speed affects the magnetic field by showing the presence of polar, azimuthal, and time components.