CONFORMALLY RICCI FLAT PURE RADIATION METRICS

Wils has recently investigated pure radiation metrics which are confor mal to a vacuum spacetime. It is shown here that, contrary to his clai m, he did not find all such solutions. The metrics he found were of ty pe N (or 0) and the conformal factor was independent of the radial coo rdinate. The form of the metric depended on whether the spin coefficie nt tau vanished or not. We find that in the tau not equal 0 case there are additional type O solutions, some of which have only a radially d ependent conformal factor and that in the tau = O case, in addition to the type N and type O solutions found by Wils, there are type III pur e radiation metrics which are conformally Ricci flat. It is proved tha t this exhausts the class of conformally Ricci flat pure radiation sol utions of Einstein's equations. For all type O solutions when tau = 0, and for some type O solutions in the tau not equal 0 case, two confor mal factors are found, one dependent on the radial coordinate, the oth er independent of it, indicating that these spaces possess a conformal symmetry.