Magnetic fields in spaces with VII0 x VIII isometries.

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 =i sinh 2 (fiz), by means of the null oblique geodesics and Penrose diagram. Finally, we derive general expressions for the A„(x;y;z)„=1;3 components of the vector potential, satisfying the source-free Maxwell equations and the Lorentz condition, pointing out the in∞uence of the global pathological properties on the behaviour of magnetostatic flelds in such universes. 1. The Geometry of the Model The properties of globally pathological manifolds and the behaviour of difierent matter sources in such universes have always been of real interest because of their implications for a better understanding of gravity and spacetime (Brans and Dicke 1961; Hoyle and Narlikar 1964; Guth 1981; Linde 1982; Collins et al. 1989). In addition to naked singularities, cosmic strings, Bianchi spacetimes, dynamical isotropisation, hollow cylinders and topological domain walls (Vilenkin and Shellard