In Minkowski space-time, (locally) space-filling families of null geodesics i.e., null geodesic congruences, appear in a variety different physical contexts. We here describe what appears to be the general explicit generic expression for these congruences. From each congruence one can construct a (virtually) unique form of the flat Lorentzian metric that is associated with the congruence. In addition, the “so-called” optical parameters for each congruence are calculated. The very important special cases of the shear-free congruences (twisting and non-twisting) are described in detail. These results are closely related to the asymptotically shear-free null geodesic congruences of asymptotically flat space-times and their rather surprising physical implications.

中文翻译：

---

平面空间零测地线同余的几何

在闵可夫斯基时空中，（局部）空测地线的空间填充族，即空测地线同余，出现在各种不同的物理环境中。我们在此描述似乎是这些同余的一般显式泛型表达式。从每个同余可以构造一个（几乎）唯一形式的与同余相关的平面洛伦兹度量。此外，计算每个同余的“所谓”光学参数。详细描述了无剪切同余（扭曲和非扭曲）的非常重要的特殊情况。这些结果与渐近平坦时空的渐近无剪切零测地线同余及其相当令人惊讶的物理意义密切相关。