Frenet-Serret formalism for null world lines

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.

arXiv comment20 pages, no figures; published version

References in corpus (3)

• The Frenet Serret Description of Gyroscopic Precession
• Circular Holonomy and Clock Effects in Stationary Axisymmetric Spacetimes
• Transport along Null Curves

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