  In this paper, we analyze the stability of a homogeneous self-gravitating
plasma, having a non-zero resistivity. This study provides a generalization of
the Jeans paradigm for determining the critical scale above which gravitational
collapse is allowed. We start by discussing the stability of an ideal
self-gravitating plasma embedded in a constant magnetic field. We outline the
existence of an anisotropic feature of the gravitational collapse. In fact,
while in the plane orthogonal to the magnetic field the Jeans length is
enhanced by the contribution of the magnetic pressure, outside this plane
perturbations are governed by the usual Jeans criterium. The anisotropic
collapse of a density contrast is sketched in details, suggesting that the
linear evolution provides anisotropic initial conditions for the non-linear
stage, where this effect could be strongly enforced. The same problem is then
faced in the presence of non-zero resistivity and the conditions for the
gravitational collapse are correspondingly extended. The relevant feature
emerging in this resistive scenario is the cancellation of the collapse
anisotropy in weakly conducting plasmas. In this case, the instability of a
self-gravitating resistive plasma is characterized by the standard isotropic
Jeans length in any directions. The limit of very small resistivity coefficient
is finally addressed, elucidating how reminiscence of the collapse anisotropy
can be found in the different value of the perturbation frequency inside and
outside the plane orthogonal to the magnetic field.
