Null geodesics in the C-metric with cosmological constant

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 $Q$ 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 $Q$. 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.

arXiv comment27 pages, 9 figures. Typos corrected and references added

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• Timelike orbits around accelerating black holes
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• Null integrability and photon phenomenology in the accelerated Schwarzschild black hole
• Conformal scalar NUT-like dyons in conformal electrodynamics
• Accelerating electrically charged ModMax black hole solutions in $F(R)$ gravity