Some Spacetimes with Higher Rank Killing-Stackel Tensors
General Relativity and Quantum Cosmology
2015-05-27 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1103.5366,
title = {Some Spacetimes with Higher Rank Killing-Stackel Tensors},
author = {G. W. Gibbons and T. Houri and D. Kubiznak and C. M. Warnick},
journal= {arXiv preprint arXiv:1103.5366},
year = {2015}
}