Killing-Yano Tensors, Rank-2 Killing Tensors, and Conserved Quantities in Higher Dimensions

Article

Killing-Yano Tensors, Rank-2 Killing Tensors, and Conserved Quantities in Higher Dimensions

Krtouš, P.; Kubizňák, D.; Page, D. N.; Frolov, V. P.

J. High Energy Phys. 0702, 4 (2007)

arXiv:hep-th/0612029 ↗

Abstract

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).

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{UTF7,
  author        = {Krtouš, P. and Kubizňák, D. and Page, D. N. and Frolov, V. P.},
  title         = {{Killing-Yano Tensors, Rank-2 Killing Tensors, and Conserved Quantities in Higher Dimensions}},
  journal       = {J. High Energy Phys.},
  volume        = {0702},
  pages         = {4},
  year          = {2007},
  month         = {2},
  eprint        = {hep-th/0612029},
  archivePrefix = {arXiv},
}