This paper reviews the concept of pp-waves and plane waves in classical general relativity theory. The first four sections give discussions of some algebraic constructions and symmetry concepts which will be needed in what is to follow. The final sections deal with the definitions of such wave solutions, their associated geometrical tensors in space–time and their Killing, homothetic, conformal and wave surface symmetries. Some unusual geometrical features of these solutions (compared with standard positive definite geometry) are described.

中文翻译：

---

广义相对论中关于波动解的一些评论

本文回顾了经典广义相对论中的pp波和平面波的概念。前四个部分讨论了一些代数构造和对称性概念，这些内容将在后续内容中讨论。最后几节讨论了此类波动解的定义，其时空相关的几何张量以及它们的Killing，同构，共形和波动表面对称性。描述了这些解决方案的一些异常几何特征（与标准的正定几何相比）。