  In vacuum space-times the exterior derivative of a Killing vector field is a
2-form (named here as the Papapetrou field) that satisfies Maxwell's equations
without electromagnetic sources. In this paper, using the algebraic structure
of the Papapetrou field, we will set up a new formalism for the study of vacuum
space-times with an isometry, which is suitable to investigate the connections
between the isometry and the Petrov type of the space-time. This approach has
some advantages, among them, it leads to a new classification of these
space-times and the integrability conditions provide expressions that determine
completely the Weyl curvature. These facts make the formalism useful for
application to any problem or situation with an isometry and requiring the
knowledge of the curvature.
