Complete Integrability of Geodesic Motion in General Kerr-NUT-AdS Spacetimes
Abstract
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.
Keywords
Cite
@article{arxiv.hep-th/0611083,
title = {Complete Integrability of Geodesic Motion in General Kerr-NUT-AdS Spacetimes},
author = {Don N. Page and David Kubiznak and Muraari Vasudevan and Pavel Krtous},
journal= {arXiv preprint arXiv:hep-th/0611083},
year = {2008}
}
Comments
4 pages. We have now found that the geodesic motion is not just integrable, but completely integrable