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Some Spacetimes with Higher Rank Killing-Stackel Tensors

By G. W. Gibbons, T. Houri, D. Kubiznak and C. M. Warnick


By applying the lightlike Eisenhart lift to several known examples of low-dimensional integrable systems admitting integrals of motion of higher-order in momenta, we obtain four- and higher-dimensional Lorentzian spacetimes with irreducible higher-rank Killing tensors. Such metrics, we believe, are first examples of spacetimes admitting higher-rank Killing tensors. Included in our examples is a four-dimensional supersymmetric pp-wave spacetime, whose geodesic flow is superintegrable. The Killing tensors satisfy a non-trivial Poisson-Schouten-Nijenhuis algebra. We discuss the extension to the quantum regime

Topics: General Relativity and Quantum Cosmology, High Energy Physics - Theory, Mathematical Physics
Year: 2011
DOI identifier: 10.1016/j.physletb.2011.04.047
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