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Within the context of general relativity we study in a fully covariant waythe so-called Euler-Maxwell system of equations. In particular, on decomposingthe aforementioned system into its 1 temporal and 1 + 2 spatial components atthe ideal magnetohydrodynamic limit, we bring it in a simplified form thatfavors physical insight to the problem of a self-gravitating, magnetized fluid.Of central interest is the decomposition of Faraday's equation which leads to anew general solution governing the evolution of the magnetic field during themotion of the highly conducting fluid. According to the latter relation, themagnetic field generally grows or decays in proportion to the inverse cube lawof the scale factor--associated with the continuous contraction or expansion ofthe fluid's volume respectively. The magnetic field's law of variation, whichhas remarkable implications for the motion of the whole fluid, is subsequentlyapplied to homogeneous (anisotropic-magnetized) cosmological models--especiallyto the Bianchi I case--as well as to the study of homogeneous and anisotropicgravitational collapse in a magnetized environment. Concerning the cosmologicalapplication, we derive the evolution equations of Bianchi I spacetime permeatedby large-scale magnetic fields (these equations reduce to their FRWcounterparts at the small/large--scale limit). Also, the compatibility of thenew evolution formula for the magnetic field with the standard cosmicnucleosynthesis constraint is examined. As for the application in astrophysics,our results predict that homogeneous gravitational implosion is impeded whenthe electric Weyl tensor (associated with tidal forces) along the magneticforcelines overwhelms the magnetic energy density. Lastly, our model denotesthat the satisfaction of the aforementioned criterion is ultimately driven intoa problem of initial conditions.

How the magnetic field behaves during the motion of a highly conducting fluid under its own gravity--A new theoretical, relativistic approach