Conformally Ricci flat pure radiation metrics

Details Conformally Ricci flat pure radiation metrics Conformally Ricci flat pure radiation metrics

Dec 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997cqgra..14.3453l&link_type=abstract

Classical and Quantum Gravity, Volume 14, Issue 12, pp. 3453-3473 (1997).

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Wils has recently investigated pure radiation metrics which are conformal to a vacuum spacetime. It is shown here that, contrary to his claim, he did not find all such solutions. The metrics he found were of type N (or O) and the conformal factor was independent of the radial coordinate. The form of the metric depended on whether the spin coefficient 0264-9381/14/12/026/img5 vanished or not. We find that in the 0264-9381/14/12/026/img6 case there are additional type O solutions, some of which have only a radially dependent conformal factor and that in the 0264-9381/14/12/026/img7 case, in addition to the type N and type O solutions found by Wils, there are type III pure radiation metrics which are conformally Ricci flat. It is proved that this exhausts the class of conformally Ricci flat pure radiation solutions of Einstein's equations. For all type O solutions when 0264-9381/14/12/026/img7, and for some type O solutions in the 0264-9381/14/12/026/img6 case, two conformal factors are found, one dependent on the radial coordinate, the other independent of it, indicating that these spaces possess a conformal symmetry.

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