Abstract
The invariant classification (Karlhede classification)1 of a particular spacetime fixes (up to isotropy) an intrinsic tetrad for the spacetime, in terms of the Riemann tensor and its derivatives. Exploiting this tetrad, it has been shown how to determine the number of Killing vectors which exist 2, and also whether a proper homothetic Killing vector exists 3. The first part of the talk outlined a procedure for finding explicitly homothetic and Killing vectors by exploiting the symmetry properties of the intrinsic tetrad 4,5. In general, it is not always possible to use this same tetrad to investigate proper conformal Killing vectors by the same methods. In this talk it was suggested to modify the invariant classification procedure so that only conformally invariant conditions are used for fixing the tetrad in terms of the Riemann tensor and its derivatives. This would mean that the existence of proper conformal Killing vectors could be deduced directly from the modified invariant classification scheme, and then found explicitly 6.
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