The effect of a non-uniform magnetic field on the gravitational instability for a non-uniformly rotating, infinitely extending axisymmetric cylinder in a homogeneous medium has been studied. The Bel and Schatzman criterion of gravitational instability for a non-uniformly rotating medium is modified under the effect of a nonuniform/uniform magnetic field acting along the tangential and axial directions. As a consequence the stabilizing and destabilizing effect of the non-uniform magnetic field is obtained, a new criterion for the magneto-gravitational instability is deduced in terms of Alfven's wave velocity; and it is also found that the Jeans criterion determines the gravitational instability in the absence of rotation and when the non-uniform/uniform magnetic field acts along the axis of the cylinder.

In the present paper, we investigate the effect of rotation on the onset of gravitational collapse and the growth rate of magnetogravitational instability of a finitely electrically conducting viscoelastic medium under both strongly and weakly coupled plasma limits for transverse and longitudinal modes of wave propagation. A general dispersion relation, which is uniformly valid for both the transverse and longitudinal mode of wave propagation, is obtained using the normal mode analysis method. It is observed that the rotation has no effect on the instability criterion which governs the onset of gravitational collapse of the viscoelastic medium in the presence of a magnetic field for either the longitudinal or transverse mode of wave propagation in strongly coupled plasma (SCP) or weakly coupled plasma (WCP). Furthermore, the effects of rotation (Coriolis force), finite electrical resistivity and shear viscosity on the growth rate of Jeans instability in both SCP and WCP for transverse modes of propagation have been numerically calculated and the results obtained are depicted graphically. From these results, we concluded that the rotation reduces the growth rate of Jeans instability.

No abstract

No abstract

No abstract