标题： 超曲面正交生成元的正交可递变换$G_2I$、拓扑识别，以及轴对称和圆柱对称时空 显示英文标题

标题： Hypersurface-orthogonal generators of an orthogonally transitive transitive $G_2I$, topological identifications, and axially and cylindrically symmetric spacetimes

摘要： 卡斯特洪-阿梅内多和麦克卡尔姆（1990）给出的一个判据，用于判断时空中的正交各向同性二参数阿贝尔运动群（一个$G_2I$）的局部超曲面正交生成器的存在性，被重新表述为一种测试条件，即测试度规在规范坐标下的轨道的三个分量之间是否存在具有常数系数的线性相关关系。 一般而言，这种关系意味着度规在规范坐标下是局部可对角化的，或者存在一个零Killing矢量，或者可以局部写成麦克因托什所描述的“风车”解的广义形式。 如果运动群$G_2I$的轨道具有圆柱状或环面状拓扑，并且使用了一个周期性坐标，则这些度规形式通常不能全局实现，因为它们会与拓扑识别产生冲突。此时几何结构还会有额外的本质参数，用以指定拓扑识别的方式。 通过全局全纯性和外部解的例子可以看出这些参数的物理意义，其中外部解中的参数已与物理源的特性相关联。 这些结果引发了一些关于圆柱对称性定义的思考。 显示英文摘要

摘要： A criterion given by Castejon-Amenedo and MacCallum (1990) for the existence of (locally) hypersurface-orthogonal generators of an orthogonally-transitive two-parameter Abelian group of motions (a $G_2I$) in spacetime is re-expressed as a test for linear dependence with constant coefficients between the three components of the metric in the orbits in canonical coordinates. In general, it is shown that such a relation implies that the metric is locally diagonalizable in canonical coordinates, or has a null Killing vector, or can locally be written in a generalized form of the `windmill' solutions characterized by McIntosh. If the orbits of the $G_2I$ have cylindrical or toroidal topology and a periodic coordinate is used, these metric forms cannot in general be realized globally as they would conflict with the topological identification. The geometry then has additional essential parameters, which specify the topological identification. The physical significance of these parameters is shown by their appearance in global holonomy and by examples of exterior solutions where they have been related to characteristics of physical sources. These results lead to some remarks about the definition of cylindrical symmetry.