INTEGRATION IN THE GHP FORMALISM .3. FINDING CONFORMALLY FLAT RADIATION METRICS AS AN EXAMPLE OF AN OPTIMAL SITUATION

Held has proposed an integration procedure within the GHP formalism bu ilt around four real, functionally independent, zero-weighted scalars. He suggests that such a procedure would be particularly simple for th e 'optimal situation', when the formalism directly supplies the full q uota of four scalars of this type; a spacetime without any Killing vec tors would be such a situation. Wils has recently obtained a conformal ly flat, pure radiation metric, which has been shown by Koutras to adm it no Killing vectors, in general. In order to present a simple illust ration of the GHP integration procedure, we obtain systematically the complete class of conformally flat, pure radiation metrics, which are not plane waves. Our result shows that the conformally fiat, pure radi ation metrics are a larger class than Wils has obtained.