The new tetrads introduced previously for non-null electromagnetic fields in Einstein–Maxwell spacetimes enable a direct link to the local electromagnetic gauge group of transformations. Due to the peculiar elements in the construction of these new tetrads, a direct connection can be established between the local group of electromagnetic gauge transformations and local groups of tetrad transformations on two different local and orthogonal planes of eigenvectors of the Einstein–Maxwell stress–energy tensor. These tetrad vectors are gauge dependent. It is an interesting and relevant problem to study if there are local gauge transformations that can map on the timelike-spacelike plane, the timelike and the spacelike vectors into the intersection of the local light cone and the plane itself. How many of these local gauge transformations exist and how the mathematics and the geometry of these particular transformations play out. These local gauge transformations would be singular and it is important to identify them.

中文翻译：

---

几何动力学中的奇异规范变换

之前为爱因斯坦-麦克斯韦时空中的非零电磁场引入的新四分体可以直接链接到局部电磁规范组的变换。由于这些新四分体构造中的特殊元素，可以在爱因斯坦-麦克斯韦应力-能量的两个不同局部和正交特征向量平面上的电磁规范变换的局部群和四分体变换的局部群之间建立直接联系张量。这些四分体向量是规范依赖的。研究是否存在可以将类时空平面、类时向量和类空向量映射到局部光锥和平面本身的交点的局部规范变换是一个有趣且相关的问题。这些局部规范变换中有多少存在以及这些特定变换的数学和几何学如何发挥作用。这些局部规范变换将是奇异的，识别它们很重要。