2008/10/31 by David Kubiznak, David Kubizňák, Valeri P. Frolov +3
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Pulsars and Gravitational Waves Research #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.79.024018
published as Phys.Rev.D79:024018,2009 · 17 pages, no figures
arxiv created 2008/10/31 · openalex publication_date 2009/01/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \mathbith were solved. The construction employed is based on studying the Darboux subspaces of the 2-form \mathbitF obtained as a projection of \mathbith 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 Pleba\ifmmode \acuten\else 'n\fiski-Demia\ifmmode \acuten\else 'n\fiski metric which admits only a conformal generalization of the Killing-Yano tensor.