  We examine the dynamics of a self--gravitating magnetized neutron gas as a
source of a Bianchi I spacetime described by the Kasner metric. The set of
Einstein-Maxwell field equations can be expressed as a dynamical system in a
4-dimensional phase space. Numerical solutions of this system reveal the
emergence of a point--like singularity as the final evolution state for a large
class of physically motivated initial conditions. Besides the theoretical
interest of studying this source in a fully general relativistic context, the
resulting idealized model could be helpful in understanding the collapse of
local volume elements of a neutron gas in the critical conditions that would
prevail in the center of a compact object.
