On the Papapetrou field in vacuum

In this paper we study the electromagnetic fields generated by a Killing ve ctor held in vacuum spacetimes (Papapetrou fields). The motivation of this work is to provide new tools for the resolution of Maxwell's equations as w ell as for the search, characterization, and study of exact solutions of Ei nstein's equations. The first part of this paper is devoted to an algebraic study in which we give an explicit and covariant procedure to construct th e principal null directions of a Papapetrou field. In the second part, we f ocus on the main differential properties of the principal directions, study ing when they are geodesic, and in that case we compute their associated op tical scalars. With this information we get the conditions that a principal direction of the Papapetrou field must satisfy in order to be aligned with a multiple principal direction of the Weyl tensor in the case of algebraic ally special vacuum spacetimes. Finally, we illustrate this study using the Ken; Kasner and pp waves spacetimes.