A new class of empty-space metrics is obtained, one member of this class being a natural generalization of the Schwarzschild metric. This latter metric contains one arbitrary parameter in addition to the mass. The entire class is the set of metrics which are algebraically specialized (contain multiple-principle null vectors) such that the propagation vector is not proportional to a gradient. These metrics belong to the Petrov class type I degenerate.

We generalize the Bondi-Sachs treatment of the initial-value problem using null coordinate systems. This treatment is applicable in both finite and asymptotic regions of space whose sources are bounded by a finite world tube. Using the conformal techniques developed by Penrose, we rederive the results of Bondi and co-workers and of Sachs in conformal-space language. Definitions of asymptotic symmetry "linkages" are developed which offer an invariant way of labeling the properties of finite regions of space, e.g., energy and momentum. These linkages form a representation of the Bondi-Metzner-Sachs asymptotic symmetry group.

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.

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