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

Article

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

Kubizňák, D.; Frolov, V. P.; Krtouš, P.; Connell, P.

Phys. Rev. D 79, 024018 (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.

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{UTF344,
  author        = {Kubizňák, D. and Frolov, V. P. and Krtouš, P. and Connell, P.},
  title         = {{Parallel-propagated frame along null geodesics in higher-dimensional black hole spacetimes}},
  journal       = {Phys. Rev. D},
  volume        = {79},
  pages         = {024018},
  year          = {2009},
  doi           = {10.1103/PhysRevD.79.024018},
  eprint        = {0811.0012},
  archivePrefix = {arXiv},
}