Parallel-propagated frame along null geodesics in higher-dimensional black hole spacetimes

David Kubizňák, Valeri P. Frolov, Pavel Krtouš, and Patrick Connell
Phys. Rev. D 79, 024018 – Published 22 January 2009

Abstract

In [arXiv:0803.3259] the equations describing the parallel transport of orthonormal frames along timelike (spacelike) geodesics in a spacetime admitting a nondegenerate principal conformal Killing-Yano 2-form h were solved. The construction employed is based on studying the Darboux subspaces of the 2-form F obtained as a projection of h along the geodesic trajectory. In this paper we demonstrate that, although slightly modified, a similar construction is possible also in the case of null geodesics. In particular, we explicitly construct the parallel-transported frames along null geodesics in D=4, 5, 6 Kerr-NUT-(A)dS spacetimes. We further discuss the parallel transport along principal null directions in these spacetimes. Such directions coincide with the eigenvectors of the principal conformal Killing-Yano tensor. Finally, we show how to obtain a parallel-transported frame along null geodesics in the background of the 4D Plebański-Demiański metric which admits only a conformal generalization of the Killing-Yano tensor.

  • Received 31 October 2008

DOI:https://doi.org/10.1103/PhysRevD.79.024018

©2009 American Physical Society

Authors & Affiliations

David Kubizňák1,2,*, Valeri P. Frolov1,†, Pavel Krtouš3,‡, and Patrick Connell1,§

  • 1Theoretical Physics Institute, University of Alberta, Edmonton, Alberta, Canada T6G 2G7
  • 2DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
  • 3Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University in Prague, V Holešovičkách 2, Prague, Czech Republic

  • *dk317@cam.ac.uk
  • frolov@phys.ualberta.ca
  • Pavel.Krtous@utf.mff.cuni.cz
  • §pconnell@phys.ualberta.ca

See Also

Solving parallel transport equations in the higher-dimensional Kerr-NUT-(A)dS spacetimes

Patrick Connell, Valeri P. Frolov, and David Kubizňák
Phys. Rev. D 78, 024042 (2008)

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Vol. 79, Iss. 2 — 15 January 2009

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