Complete Integrability of Geodesic Motion in General Higher-Dimensional Rotating Black Hole Spacetimes

Article

Complete Integrability of Geodesic Motion in General Higher-Dimensional Rotating Black Hole Spacetimes

Page, D. N.; Kubizňák, D.; Vasudevan, M.; Krtouš, P.

Phys. Rev. Lett. 98, 061102 (2007)

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.

Institute authors

Krtouš, Pavel

Supported by

GACR 202/06/0041 — Contemporary problems of general relativity and gravitation
MSM0021620860 — Fyzikální studium objektů a procesů ve sluneční soustavě a v astro-fyzikálních systémech

BibTeX

@article{UTF9,
  author        = {Page, D. N. and Kubizňák, D. and Vasudevan, M. and Krtouš, P.},
  title         = {{Complete Integrability of Geodesic Motion in General Higher-Dimensional Rotating Black Hole Spacetimes}},
  journal       = {Phys. Rev. Lett.},
  volume        = {98},
  pages         = {061102},
  year          = {2007},
  eprint        = {hep-th/0611083},
  archivePrefix = {arXiv},
}