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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.
Newman et al. (Sat,) studied this question.