The invariant classification of conformally flat pure radiation spacetimes

We study conformally Bat pure radiation spacetimes by means of their invariant classifications and show that no such spacetime requires higher than the fourth covariant derivative of the Riemann tensor in its invariant classification. Additional side results that we obtain are as follows. The Edgar-Ludwig metric for conformally Bat pure radiation is shown to be a true generalization of the Wils metric; the subclass of the Edgar-Ludwig spacetimes which admit exactly one Killing vector is identified, generalizing Koutras's G1 subclass of the Wils metric; it is shown that the Edgar-Ludwig spacetimes with no Killing vectors can further be split into three discrete subsets, depending on the Cartan invariant where the fourth essential coordinate is found.