  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.
