Null geodesics in the C-metric with cosmological constant
arXiv:2011.05503 · doi:10.1103/PhysRevD.103.024007
Abstract
In this paper we study the motion of photons or massless particles in the C-metric with cosmological constant. The Hamilton--Jacobi equations are known to be completely separable, giving a Carter-like quantity which is a constant of motion. All possible trajectories are classified according to a two-dimensional parameter space representing the particle's angular momentum and energy scaled in units of . Exact solutions are given in the C-metric coordinates in terms of Jacobi elliptic functions. Using the exact solutions, we find examples of periodic orbits on the photon surface.
27 pages, 9 figures. Typos corrected and references added
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