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The C-metric is a solution to Einstein's vacuum field equation that describesan accelerating black hole. In this paper we discuss the propagation of lightrays and the resulting lensing features in this metric. We first solve thelightlike geodesic equation using elliptic integrals and Jacobi ellipticfunctions. Then we fix a static observer in the region of outer communicationof the C-metric and introduce an orthonormal tetrad to parameterise thedirections of the light rays ending at the position of the observer usinglatitude-longitude coordinates on the observer's celestial sphere. In thisparameterisation we rederive the angular radius of the shadow, we formulate alens equation, and we derive the redshift and the travel time of light rays. Wediscuss the relevance of our theoretical results for detecting acceleratingblack holes described by the C-metric and for distinguishing them fromnon-accelerating black holes.

Lightlike Geodesics and Gravitational Lensing in the Spacetime of an Accelerating Black Hole