Parallel-propagated frame along null geodesics in higher-dimensional black hole spacetimes
Kubizňák, D.; Frolov, V. P.; Krtouš, P.; Connell, P.
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.
type: | article |
journal: | Phys. Rev. D |
volume: | 79 |
pages: | 024018 |
year: | 2009 |
eprint: | arXiv:0811.0012 |
grants: | Contemporary problems of general relativity and gravitation, GAČR 202/06/0041; 2006-2008; hlavní řešitel: Jiří BičákFyzikální studium objektů a procesů ve sluneční soustavě a v astro-fyzikálních systémech, výzkumný záměr MSM0021620860; 2007-2013; hlavní řešitel: Jiří Bičák |