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

Don N. Page, David Kubizňák, Muraari Vasudevan, and Pavel Krtouš
Phys. Rev. Lett. 98, 061102 – Published 9 February 2007

Abstract

We explicitly exhibit n1=[D/2]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 (D2)-dimensional Killing-Yano tensor. These constants of motion are functionally independent of each other and of the Dn+1 constants of motion that arise from the metric and the Dn=[(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.

  • Received 9 November 2006

DOI:https://doi.org/10.1103/PhysRevLett.98.061102

©2007 American Physical Society

Authors & Affiliations

Don N. Page1,*, David Kubizňák1,3,†, Muraari Vasudevan1,2,‡, and Pavel Krtouš3,§

  • 1Theoretical Physics Institute, University of Alberta, Edmonton, Alberta, Canada T6G 2G7
  • 2JLR Engineering, 111 SE Everett Mall Way, E-201, Everett, Washington 98208-3236, USA
  • 3Institute of Theoretical Physics, Charles University, V Holešovičkách 2, Prague, Czech Republic

  • *Electronic address: don@phys.ualberta.ca
  • Electronic address: kubiznak@phys.ualberta.ca
  • Electronic address: mvasudev@phys.ualberta.ca
  • §Electronic address: Pavel.Krtous@mff.cuni.cz

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Issue

Vol. 98, Iss. 6 — 9 February 2007

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