Parallel-propagated frame along null geodesics in higher-dimensional black hole spacetimes
- Theoretical Physics Institute, University of Alberta, Edmonton, Alberta, T6G 2G7 (Canada)
- Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University in Prague, V Holesovickach 2, Prague (Czech Republic)
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 Plebanski-Demianski metric which admits only a conformal generalization of the Killing-Yano tensor.
- OSTI ID:
- 21259813
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 79, Issue 2; Other Information: DOI: 10.1103/PhysRevD.79.024018; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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