Magnetic fields and the Weyl tensor in the early universe
  We have solved the Einstein-Maxwell equations for a class of isotropic metrics with constant spatial curvature in the presence of magnetic fields. We consider a slight modification of the Tolman averaging relations so that the energy-momentum tensor of the electromagnetic field possesses an anisotropic pressure component. This inhomogeneous magnetic universe is isotropic and its time evolution is guided by the usual Friedmann equations. In the case of flat universe, the space-time metric is free of singularities (except the well-known initial singularity at t = 0). It is shown that the anisotropic pressure of our model has a straightforward relation to the Weyl tensor. We also analyze the effect of this new ingredient on the motion of test particles and on the geodesic deviation of the cosmic fluid. 
Eduardo Bittencourt, Jos\'e Salim and Grasiele B. dos Santos
gr-qc astro-ph.CO