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Held has proposed an integration procedure within the GHP formalism builtaround four real, functionally independent, zero-weighted scalars. He suggeststhat such a procedure would be particularly simple for the `optimal situation',when the formalism directly supplies the full quota of four scalars of thistype; a spacetime without any Killing vectors would be such a situation. Wilshas recently obtained a metric which he claims is the only conformally flat,pure radiation metric which is not a plane wave; this metric has been shown byKoutras to admit no Killing vectors, in general. Therefore, as a simpleillustration of the GHP integration procedure, we obtain systematically thecomplete class of conformally flat, pure radiation metrics. Our result showsthat the conformally flat, pure radiation metrics, which are not plane waves,are a larger class than Wils has obtained.Comment: 22 pages, plain Te

Integration in the GHP Formalism III: Finding Conformally Flat Radiation Metrics as an Example of an “Optimal Situation”