  Within the context of general relativity we study in a fully covariant way
the so-called Euler-Maxwell system of equations. In particular, on decomposing
the aforementioned system into its 1 temporal and 1 + 2 spatial components at
the ideal magnetohydrodynamic limit, we bring it in a simplified form that
favors physical insight to the problem of a self-gravitating, magnetized fluid.
Of central interest is the decomposition of Faraday's equation which leads to a
new general solution governing the evolution of the magnetic field during the
motion of the highly conducting fluid. According to the latter relation, the
magnetic field generally grows or decays in proportion to the inverse cube law
of the scale factor--associated with the continuous contraction or expansion of
the fluid's volume respectively. The magnetic field's law of variation, which
has remarkable implications for the motion of the whole fluid, is subsequently
applied to homogeneous (anisotropic-magnetized) cosmological models--especially
to the Bianchi I case--as well as to the study of homogeneous and anisotropic
gravitational collapse in a magnetized environment. Concerning the cosmological
application, we derive the evolution equations of Bianchi I spacetime permeated
by large-scale magnetic fields (these equations reduce to their FRW
counterparts at the small/large--scale limit). Also, the compatibility of the
new evolution formula for the magnetic field with the standard cosmic
nucleosynthesis constraint is examined. As for the application in astrophysics,
our results predict that homogeneous gravitational implosion is impeded when
the electric Weyl tensor (associated with tidal forces) along the magnetic
forcelines overwhelms the magnetic energy density. Lastly, our model denotes
that the satisfaction of the aforementioned criterion is ultimately driven into
a problem of initial conditions.
