On space-time permeated by the perfect magnetofluid

A space-time permeated by the self-gravitating perfect fluid with infinite electrical conductivity and constant magnetic permeability (perfect magnetofluid) is investigated. For aC space defined as the space in which the divergence of conformal curvature vanishes, it is proved that the rotation explicitly depends on the magnetic field. In aJ space characterized by the vanishing of the divergence of Petrov space-matter tensor, the invariance of the energy density, the isotropic pressure, and the magnitude of the magnetic field along the divergence-free magnetic lines is established. It is found that if the stress-energy tensor of the perfect magnetofluid is a Killing tensor, the energy density, the isotropic pressure, and the magnitude of the magnetic field are constant. Moreover it is shown that the stream lines are expansion-free and the magnetic lines are divergence-free. It is proved that the complexion of the field of the perfect magnetofluid remains invariant along the magnetic lines if and only if these lines are normal to the lines of vorticity.