Plasma modes along the open field lines of a neutron star

We consider electrostatic plasma modes along the open held lines of a rotat ing neutron star. Goldreich-Julian charge density in general relativity is analyzed for the neutron star with zero inclination. It is found that the c harge density is maximum at the polar cap and remains almost the same in a certain extended region of the pole. For a steady state Goldreich-Julian ch arge density we found the usual plasma oscillation along the field lines; p lasma frequency resembles the gravitational redshift close to the Schwarzsc hild radius. We study the nonlinear plasma mode along the held lines. From the system of equations under general relativity, a second-order differenti al equation is derived. The equation contains a term that describes the gro wing plasma modes near Schwarzschild radius in a black hole environment. Th e term vanishes with the distance far away from the gravitating object. For initially zero potential and held on the surface of a neutron star, Goldre ich-Julian charge density is found to create the plasma mode, which is enha nced and propagates almost without damping along the open held lines. We br iefly outline our plan to extend the work far studying soliton propagation along the open field lines of strongly gravitating objects.