2002/12/03 by A. Barnes, Alan Barnes, S. B. Edgar +4
Physics and Astronomy · #Advanced Differential Geometry Research #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0212016
5 pages, Latex. To appear in the Proceedings of the Spanish Relativity Meeting (Encuentros Relativistas Espanoles), 2002
arxiv created 2002/12/03 · openalex publication_date 2002/12/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.