Null geodesics in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi></mml:math> metric with a cosmological constant

In this paper we study the motion of photons or massless particles in $C$ metric with cosmological constant. The Hamilton-Jacobi equations are known to be completely separable, giving a Carter-like quantity $Q$ which is constant motion. All possible trajectories classified according two-dimensional parameter space representing particle's angular momentum and energy scaled units $Q$. Exact solutions given coordinates terms Jacobi elliptic functions. Using exact solutions, find examples periodic orbits on photon surface.