Magnetic fields in spaces with VII0 x VIII isometries.

Abstract

The aim of the present paper is to investigate some globally pathological features of a class of static planary symmetric exact solutions with a G₆-group of motion, namely with g44 = –sinh² (αz), by means of the null oblique geodesics and Penrose diagram. Finally, we derive general expressions for the Aµ(x, y, z)µ=_1,3― components of the vector potential, satisfying the source-free Maxwell equations and the Lorentz condition, pointing out the influence of the global pathological properties on the behaviour of magnetostatic fields in such universes.