Killing tensors and conformai Killing tensors from conformal Killing vectors

Koutras 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 restrict...

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Bibliographic Details
Published in:Classical and quantum gravity 2003-06, Vol.20 (11), p.1929
Main Authors: Rani, Raffaele, Edgar, S. Brian, Barnes, A.
Format: Article
Language:English
Subjects:
TECHNOLOGY
TEKNIKVETENSKAP
Online Access:Get full text
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Summary:Koutras 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.
ISSN:0264-9381
1361-6382
DOI:10.1088/0264-9381/20/11/301