Empty Space Metrics Containing Hypersurface Orthogonal Geodesic Rays

In this paper we obtain all empty space metrics which possess hypersurface orthogonal geodesic rays with nonvanishing shear and divergence. By straightforward integration of the Newman‐Penrose equations, which are equivalent to the Einstein equations, all solutions are found in closed form and are unique up to a few arbitrary constants. The method of integration is illustrated in detail for the Robinson‐Trautman solutions.