Some Spacetimes with Higher Rank Killing-Stackel Tensors

Understand

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.