Some Spacetimes with Higher Rank Killing-Stackel Tensors

Abstract

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.

References in corpus (3)

• Quantum integrability of quadratic Killing tensors
• Eisenhart's theorem and the causal simplicity of Eisenhart's spacetime
• Kovalevskaya Top and Generalizations of Integrable Systems

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