Goryachev-Chaplygin, Kovalevskaya, and Brdi\v{c}ka-Eardley-Nappi-Witten pp-waves spacetimes with higher rank St\"ackel-Killing tensors

TL;DR

This paper investigates hidden symmetries in specific spacetimes, revealing higher rank Stäckel-Killing tensors and their associated symmetry groups, which enhances understanding of spacetime symmetries in general relativity.

Contribution

The study identifies higher rank Stäckel-Killing tensors in Goryachev-Chaplygin, Kovalevskaya, and Brdička-Eardley-Nappi-Witten spacetimes, linking them to known symmetry groups.

Findings

Presence of higher rank Stäckel-Killing tensors in studied spacetimes

Symmetry group for pp-wave spacetimes is the Newton-Hooke group

Enhanced understanding of hidden symmetries in these spacetimes

Abstract

Hidden symmetries of the Goryachev-Chaplygin and Kovalevskaya gyrostats spacetimes, as well as the Brdi\v{c}ka-Eardley-Nappi-Witten pp-waves are studied. We find out that these spacetimes possess higher rank St\"ackel-Killing tensors and that in the case of the pp-wave spacetimes the symmetry group of the St\"ackel-Killing tensors is the well-known Newton-Hooke group.