Complete Integrability of Geodesic Motion in General Kerr-NUT-AdS Spacetimes

Details Complete Integrability of Geodesic Motion in General Kerr-NUT-AdS Spacetimes Complete Integrability of Geodesic Motion in General Kerr-NUT-AdS Spacetimes

2006-11-08

arxiv.org/abs/hep-th/0611083v3

Phys.Rev.Lett.98:061102,2007

Physics

High Energy Physics

High Energy Physics - Theory

4 pages. We have now found that the geodesic motion is not just integrable, but completely integrable

Scientific paper

10.1103/PhysRevLett.98.061102

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.

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