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arXiv · 1408.4281

Frenet-Serret formalism for null world lines

Donato Bini·Andrea Geralico·Robert T. Jantzen
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Abstract

The Frenet-Serret curve analysis is extended from nonnull to null trajectories in a generic spacetime using the Newman-Penrose formalism, recovering old results which are not well known and clarifying the associated Fermi-Walker transport which has been left largely unexplored in the literature. This machinery is then used to discuss null circular orbits in stationary axisymmetric spacetimes using the Kerr spacetime as a concrete example, and to integrate the equations of parallel transport along null geodesics in any spacetime.

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Donato Bini, Andrea Geralico, Robert T. Jantzen. 2014-08-19. Frenet-Serret formalism for null world lines. https://doi.org/10.1088/0264-9381%2F23%2F11%2F018

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