Einstein–Maxwell equations and the conformal Ricci collineations

Abstract

The Einstein–Maxwell field equations for non-null electromagnetic fields are studied under the assumption of admitting a conformal Ricci collineation. It is shown that a non-null electromagnetic field does not admit any conformal Ricci collineation, unless the generators of the symmetry groups are Killing vector fields. Furthermore, it is shown that the energy-momentum tensor of a non-null electromagnetic field can admit a conformal Ricci collineation, if and only if the collineation is homothetic. The restrictions on non-null Maxwell field, its sources, and its invariants implied by the symmetry condition are calculated. An example of a space-time satisfying the Einstein–Maxwell equations, and admitting a homothetic conformal vector field is also given.