Metrics obtained by integrating within the generalised invariant formalismare structured around their intrinsic coordinates, and this considerablysimplifies their invariant classification and symmetry analysis. We illustratethis by presenting a simple and transparent complete invariant classificationof the conformally flat pure radiation metrics (except plane waves) in suchintrinsic coordinates; in particular we confirm that the three apparentlynon-redundant functions of one variable are genuinely non-redundant, and easilyidentify the subclasses which admit a Killing and/or a homothetic Killingvector. Most of our results agree with the earlier classification carried outby Skea in the different Koutras-McIntosh coordinates, which required much moreinvolved calculations; but there are some subtle differences. Therefore, wealso rework the classification in the Koutras-McIntosh coordinates, and bypaying attention to some of the subtleties involving arbitrary functions, weare able to obtain complete agreement with the results obtained in intrinsiccoordinates. In particular, we have corrected and completed statements andresults by Edgar and Vickers, and by Skea, about the orders of Cartaninvariants at which particular information becomes available.
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