Homogeneous Electromagnetic and Massive-Vector Fields in Bianchi Cosmologies

Abstract

We investigate the consequences of (a) the source-free Maxwell equations and (b) the equations of massive-vector-meson fields in spatially homogeneous Bianchi cosmologies. Ve obtain explicit formulae for the electromagnetic field and its stress-energy tensor in the case where the Poynting vector vanishes. In the case of a pure magnetic (or electric) field, we show that Bianchi Types I, II, III, VI (h = - 1), and VII (I' = 0) admit only constrained field components, whereas Types IV, V, VI (k # - 1), VII (h s 0), VIII, and IX admit no field components. We find that d?agrnial Bianchi cosmologies with a massive-vector-meson field can exist only for Bianchi Types I, II, VI (h = - 1), VII (h = 0), VIII, and IX.