Publikace ÚTF

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.
typ:article
journal:Phys. Rev. D
volume:79
pages:024018
year:2009
pacs:04.50.-h, 02.40.-k, 04.20.Jb, 04.50.Gh
eprint:arXiv:0811.0012
odkaz:
files:
ptnghdbh-prd.pdf (266.94 kB)
ptnghdbh-prd.ps (606.66 kB)

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