Killing Tensors and Conformal Killing Tensors from Conformal Killing Vectors

Details Killing Tensors and Conformal Killing Tensors from Conformal Killing Vectors Killing Tensors and Conformal Killing Tensors from Conformal Killing Vectors

2003-01-16

arxiv.org/abs/gr-qc/0301059v3

Class.Quant.Grav. 20 (2003) 1929-1942

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages References added. Comments and reference to 2-dim case. Typos corrected

Scientific paper

10.1088/0264-9381/20/11/301

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 how 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 (including all the Killing tensors which will in general be irreducible) of conformally flat spaces using their conformal Killing vectors.

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