Some Spacetimes with Higher Rank Killing-Stackel Tensors

2011/03/28 by G. W. Gibbons, T. Houri, D. Kubiznak +1 · 2 citations
Physics and Astronomy · Mathematics · #gr-qc #hep-th #math-ph #math.MP

paper · pdf · doi:10.1016/j.physletb.2011.04.047

published as Phys.Lett. B700:68-74,2011

arxiv created 2011/03/28 · arxiv updated 2015/05/27

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.

Cited by

• The Bohlin variant of the Eisenhart lift
• On a lower-dimensional Killing vector origin of irreducible Killing tensors