On generation of dark solitons by gravitational waves in a strongly magnetized pulsar plasma

Abstract

In this paper, the propagation of gravitational wave perpendicular to a superstrong magnetic field immersed in an electron-positron pulsar plasma is considered. On the basis of the Einstein–Maxwell system of magnetohydrodynamic equations, both the linear and nonlinear interactions of the wave with plasma are investigated. In near-resonant interaction, a relation between gravitation perturbations to electromagnetic field perturbations shows that the field perturbations are directly proportional to the product of ambient magnetic field and the gravitational wave perturbation. Thus, a weak gravitational wave may resonate an effective field perturbation in the strongly magnetized plasma in an astrophysical context. A coupled system of equations describing the nonlinear interaction between gravitational wave and field perturbations in the magnetized plasma is obtained. The equations are solved in resonant approximation, and it is found that a linearly polarized electric field is generated with a frequency close to the plasma frequency. For nonresonant interaction, the solution shows that both electric and magnetic field perturbations in the plasma are produced. Density perturbation and field intensity variation in the plasma lead to a nonlinear frequency shift and the slowly varying field amplitude obeys the nonlinear Schrödinger equation. The solution of the equation is the dark soliton, the amplitude of which may be very significant in the case of a superstrong magnetic field in the pulsar plasma.