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Some spacetimes with higher rank Killing–Stäckel tensors

Some spacetimes with higher rank Killing–Stäckel tensors,10.1016/j.physletb.2011.04.047,Fuel and Energy Abstracts,G. W. Gibbons,T. Houri,D. Kubizňák,C

Some spacetimes with higher rank Killing–Stäckel tensors  
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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.
Journal: Fuel and Energy Abstracts , vol. 700, no. 1, pp. 68-74, 2011
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