All stationary vacuum metrics with shearing geodesic eigenrays

The general solution of the field equations of stationary vacuum gravitational fields possessing geodesic eigenrays with nonvanishing shear is obtained. Nontrivial solutions exist only if the eigenrays do not rotate. The resulting metrics fall into two classes: either there is a functional dependence among the field quantities (this class belongs to the Papapetrou solutions), or the quantity γ0, which in the shear-free case has been interpreted as the central mass, is uniquely determined. This latter class consists of two space-times. The curvature invariants vanish in the r→∞ limit for both solutions; however, the metrics exhibit singular behavior in this limit.