The C-metric is a solution to Einstein’s vacuum field equation that describes an accelerating black hole. In this paper we discuss the propagation of light rays and the resulting lensing features in this metric. We first solve the lightlike geodesic equation using elliptic integrals and Jacobi elliptic functions. Then we fix a static observer in the region of outer communication of the C-metric and introduce an orthonormal tetrad to parameterise the directions of the light rays ending at the position of the observer using latitude-longitude coordinates on the observer’s celestial sphere. In this parameterisation we rederive the angular radius of the shadow, we formulate a lens equation, and we derive the redshift and the travel time of light rays. We discuss the relevance of our theoretical results for detecting accelerating black holes described by the C-metric and for distinguishing them from non-accelerating black holes.

C-metric 是爱因斯坦真空场方程的一个解，描述了一个加速的黑洞。在本文中，我们讨论了光线的传播以及由此度量产生的透镜特征。我们首先使用椭圆积分和雅可比椭圆函数求解类似光的测地线方程。然后我们在 C-metric 的外部通信区域固定一个静态观察者，并引入一个正交四分体来参数化在观察者位置结束的光线方向，使用观察者天球上的经纬度坐标。在这个参数化中，我们重新推导了阴影的角半径，我们制定了一个透镜方程，我们推导了红移和光线的传播时间。