Abstract
This paper investigates the relationship between Killing Tensors and separable systems for the geodesic Hamilton-Jacobi equation in Riemannian and Lorentzian manifolds: locally, a separable system consists of the vector and covector associated with a separable coordinate. It is shown that there are only two types of separable system, those associated with local symmetry groups and those which can be obtained by a simple transformation from orthogonal systems. Some sufficient conditions for existence are given and some global problems are enumerated. The results are illustrated with a demonstration that the existence of separable systems in a certain class of {2, 2} space-times is a consequence of the algebraic properties of the Weyl tensor.
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Communicated by J. Ehlers
Research supported by the Science Research Council.
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Woodhouse, N.M.J. Killing tensors and the separation of the Hamilton-Jacobi equation. Commun.Math. Phys. 44, 9–38 (1975). https://doi.org/10.1007/BF01609055
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DOI: https://doi.org/10.1007/BF01609055