This paper considers a general set of Einstein–Maxwell fields in 2 + 1-dimensional space. Two broad categories of solutions are discussed, namely solutions of vanishing covariant derivatives (uniform electromagnetic fields) and stationary cyclic symmetric spaces. Subsequently, several major subclasses of solutions arise that may be classified according to the conformal algebra they possess. A key feature of these algebras is the presence of the \({\text {SO}}(2)\times R\) Killing group. It is shown that this group and other elements of the conformal algebra of each solution satisfy a special contingency relation with the potential function of the Klein–Gordon equation.

本文考虑了二维+1维空间中的爱因斯坦-麦克斯韦场的一般集合。讨论了两大类解，即消失的协变导数（均匀电磁场）和平稳循环对称空间的解。随后，出现了几种主要的解决方案子类，可以根据它们拥有的保形代数进行分类。这些代数的关键特征是\（{\ text {SO}}（2）\ times R \） Killing组的存在。结果表明，该组和每个解的共形代数的其他元素与Klein-Gordon方程的势函数满足特殊的权变关系。