Dynamics of a self-gravitating magnetized source

We consider a magnetized degenerate gas of fermions as the matter source of a homogeneous but anisotropic Bianchi I space-time with a Kasner-like metric. We examine the dynamics of this system by means of a qualitative and numerical study of Einstein-Maxwell field equations which reduce to a non-linear autonomous system. For all initial conditions and combinations of free parameters, the gas evolves from an initial anisotropic singularity into an asymptotic state that is completely determined by a stable attractor. Depending on the initial conditions the anisotropic singularity is of the "cigar" or "plate" types.