Goryachev-Chaplygin, Kovalevskaya, and Brdička-Eardley-Nappi-Witten pp-waves spacetimes with higher rank Stäckel-Killing tensors

Abstract

Hidden symmetries of the Goryachev-Chaplygin and Kovalevskaya gyrostats spacetimes, as well as the Brdička-Eardley-Nappi-Witten pp-waves are studied. We find out that these spacetimes possess higher rank Stäckel-Killing tensors and that in the case of the pp-wave spacetimes the symmetry group of the Stäckel-Killing tensors is the well-known Newton-Hooke group.

11 pages; accepted for publication in JMP

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• Some metrics admitting nonpolynomial first integrals of the geodesic equation
• Massless geodesics in $Ad{S}_5\times Y(p,q)$ as a superintegrable system
• The Bohlin variant of the Eisenhart lift