Plasma modes along the open field lines of a neutron star

We consider electrostatic plasma modes along the open field lines of a rotating neutron star. Goldreich-Julian charge density in general relativity is analyzed for the neutron star with zero inclination. It is found that the charge 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 charge density we found the usual plasma oscillation along the field lines; plasma frequency resembles the gravitational redshift close to the Schwarzschild radius. We study the nonlinear plasma mode along the held lines. From the system of equations under general relativity, a second-order differential equation is derived. The equation contains a term that describes the growing plasma modes near Schwarzschild radius in a black hole environment. The term vanishes with the distance far away from the gravitating object. For initially zero potential and held on the surface of a neutron star, Goldreich-Julian charge density is found to create the plasma mode, which is enhanced and propagates almost without damping along the open field lines. We briefly outline our plan to extend the work far studying soliton propagation along the open field lines of strongly gravitating objects.