Complete Integrability of Geodesic Motion in General Higher-Dimensional Rotating Black Hole Spacetimes
Page, D. N.; Kubizňák, D.; Vasudevan, M.; Krtouš, P.
We explicitly exhibit n-1 constants of motion for geodesics in the general D-dimensional Kerr-NUT-AdS rotating black hole spacetime, arising from contractions of even powers of the 2-form obtained by contracting the geodesic velocity with the dual of the contraction of the velocity with the (D-2)-dimensional Killing-Yano tensor. These constants of motion are functionally independent of each other and of the D-n+1 constants of motion that arise from the metric and the D-n = [(D+1)/2] Killing vectors, making a total of D independent constants of motion in all dimensions D. The Poisson brackets of all pairs of these D constants are zero, so geodesic motion in these spacetimes is completely integrable.
type: | article |
journal: | Phys. Rev. Lett. |
volume: | 98 |
pages: | 061102 |
year: | 2007 |
eprint: | hep-th/0611083 |
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 |