We discuss the propagation of light in the C-metric. We discover that null geodesics admit circular orbits only for a certain family of orbital cones. Explicit analytic formulae are derived for the orbital radius and the corresponding opening angle fixing the cone. Furthermore, we prove that these orbits based on a saddle point in the effective potential are Jacobi unstable. This completes the stability analysis done in previous literature and allows us to probe into the light bending in a two black hole metric. More precisely, by constructing a suitable tetrad in the Newmann-Penrose formalism, we show that light propagation in this geometry is shear-free, irrotational, and a light beam passing by a C-black hole undergoes a focussing process. An exact analytic formula for the compression factor $\theta$ is derived and discussed. Furthermore, we study the weak and strong gravitational lensing when both the observer and the light ray belong to the aforementioned family of invariant cones. In particular, we obtain formulae allowing to calculate the deflection angle in the weak and strong gravitational lensing regimes.

中文翻译：

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两个黑洞度量中的光弯曲

我们讨论光在 C 度量中的传播。我们发现零测地线只允许特定轨道锥族的圆形轨道。推导出轨道半径和固定锥体对应的张角的显式解析公式。此外，我们证明这些基于有效势中鞍点的轨道是雅可比不稳定的。这完成了之前文献中所做的稳定性分析，并使我们能够探索两个黑洞度量中的光弯曲。更准确地说，通过在 Newmann-Penrose 形式主义中构建一个合适的四分体，我们表明在这个几何中的光传播是无剪切的、无旋转的，并且穿过 C 黑洞的光束经历了一个聚焦过程。推导出并讨论了压缩因子 $\theta$ 的精确解析公式。此外，当观察者和光线都属于上述不变锥家族时，我们研究了弱引力透镜和强引力透镜。特别是，我们获得了允许计算弱引力透镜和强引力透镜状态下的偏转角的公式。