Raffaele Rani et al 2003 Class. Quantum Grav. 20 1929 doi:10.1088/0264-9381/20/11/301
Raffaele Rani1,3, S Brian Edgar1 and Alan Barnes2
Show affiliationsKoutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely general result demonstrating that this severe restriction of orthogonality is unnecessary. In addition, we correct and extend some results concerning Killing tensors constructed from a single conformal Killing vector. A number of examples demonstrate that it is possible to construct a much larger class of reducible proper conformal Killing tensors and Killing tensors than permitted by the Koutras algorithms. In particular, by showing that all conformal Killing tensors are reducible in conformally flat spaces, we have a method of constructing all conformal Killing tensors, and hence all the Killing tensors (which will in general be irreducible) of conformally flat spaces using their conformal Killing vectors.
Issue 11 (7 June 2003)
Received 23 January 2003
Published 1 May 2003
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