Killing Tensors from Conformal Killing Vectors
نویسندگان
چکیده
Some years ago Koutras presented a method of constructing a conformal Killing tensor from a pair of orthogonal conformal Killing vectors. When the vector associated with the conformal Killing tensor is a gradient, a Killing tensor (in general irreducible) can then be constructed. In this paper it is shown that the severe restriction of orthogonality is unnecessary and thus it is possible that many more Killing tensors can be constructed in this way. We also extend, and in one case correct, some results on Killing tensors constructed from a single conformal Killing vector. Weir’s result that, for flat space, there are 84 independent conformal Killing tensors, all of which are reducible, is extended to conformally flat spacetimes. In conformally flat spacetimes it is thus possible to construct all the conformal Killing tensors and in particular all the Killing tensors (which in general will not be reducible) from conformal Killing vectors.
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S. Brian EDGAR †, Rafaelle RANI ‡ and Alan BARNES § † Department of Mathematics, Linköping University, Linköping, Sweden S581-83 E-mail: [email protected] ‡ Institute of Astronomy and Astrophysics, Department of Theoretical Astrophysics, University of Tübingen, D-72076 Tübingen, Germany E-mail: [email protected] § School of Engineering & Applied Science, Aston University, Birmingh...
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