SPACELIKE MOTIONS ADMITTED BY THE MAGNETOFLUID SPACE-TIMES

In this paper we have obtained a set of necessary and sufficient conditions for the existence of a spacelike Killing vector collinear to the magnetic-field vector. Using these conditions, we have shown that the rotation of the congruence of magnetic-field lines is Lie invariant (or «frozen-in») for the rotating «stiff» magnetic-field lines. Furthermore, we have investigated a set of necessary and sufficient conditions for the spacelike homothetic Killing vector collinear to the magnetic-field vector. It is observed that the spacelike proper homothetic motion along the congruence of magnetic-field lines is not possible in a space of constant curvature filled with a self-gravitating magnetofluid. © 1979 Società Italiana di Fisica.