Electrodynamic instability of a self-gravitating dielectric fluid cylinder embedded in a different dielectric self-gravitating fluid

Abstract

The electrodynamic instability of a gravitational dielectric fluid cylinder embedded in a different self-gravitating infinite fluid is developed. The eigenvalue relation, valid to all symmetric and asymmetric modes, is derived and is based on the linear perturbation technique. Recent reported work is recovered as limiting case from the present result. The electric field has no direct influence on the gravitational instability of the present model. That is not only because no volume and surface charges are assumed to be present in the bulk and at the interface of the fluids but also because the electrodynamic forces acting on the fluids cancel each other, whether the pervading longitudinal electric fields are different or not. Gravitationally the model is marginally stable if the density of the cylinder is equal to that of the surrounding dielectric fluid. If the cylinder is less dense, the system is purely unstable for all (long and short!) wavelengths and the instability domains have their maximum temporal amplifications and critical wave numbers at infinity. If the cylinder is ambient with self-gravitating vacuum, the electrodynamic stabilizing influence can suppress the gravitational instability and stability arises. These results are confirmed numerically and interpreted physically.