Killing-Yano Tensors, Rank-2 Killing Tensors, and Conserved Quantities in Higher Dimensions
Krtouš, P.; Kubizňák, D.; Page, D. N.; Frolov, V. P.
From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k=[(D+1)/2] Killing-Yano tensors, of rank D-2j for all j=0,...,k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245).
type: | article |
journal: | J. High Energy Phys. |
volume: | 0702 |
pages: | 4 |
year: | 2007 |
month: | 2 |
eprint: | hep-th/0612029 |
grants: | Contemporary problems of general relativity and gravitation, GAČR 202/06/0041; 2006-2008; hlavní řešitel: Jiří BičákFyzikální studium objektů a procesů ve sluneční soustavě a v astro-fyzikálních systémech, výzkumný záměr MSM0021620860; 2007-2013; hlavní řešitel: Jiří Bičák |