Electrovac fields with geodesic eigenrays

Abstract

The stationary states of electrovac fields for which the geodesic eigenrays of both the Maxwell and gravitational field coincide are investigated. The fact that the Kerr-Newman solutions belong to this class lends physical interest to the fields considered here. Particular attention is devoted to fields with shearing eigenrays since principal null congruences do not coincide with eigenrays in this case, and so earlier approaches to the problem fail. By the generalisation of a theorem on the corresponding vacuum case, it is proven that no ‘spherical’ solutions exist in the shearing class, with the exception of the fields with γ²≡¦G_O¦²-¦H_O¦²=O.The metrics with γ≠O, admitted by the theorem, can either be calculated from the corresponding vacuum solutions by a relatively simple procedure, or, if not, we list them explicitly in this paper.