标题： 三维静态循环对称爱因斯坦-麦克斯韦解；黑洞 显示英文标题

标题： Three dimensional stationary cyclic symmetric Einstein-Maxwell solutions; black holes

摘要： 从一个用于静态循环对称引力场与麦克斯韦电磁场耦合的$(2+1)$维引力的一般度量出发，建立了广泛类别的精确解的唯一性，其中包括所有具有零协变导数的电磁场的均匀电磁解，所有具有常电磁不变量$F_{\mu\nu}\,F^{\mu\nu}$和$T_{\mu\nu}\,T^{\mu\nu}$的场，整个混合电磁解类，以及第三阶非线性关键方程的广泛静止解类。这些族中的一些可以被认为是黑洞解。对于最一般的爱因斯坦-麦克斯韦方程组，可简化为三个未知函数的三个非线性方程，推导出了两个新的解类——具有反德西特旋转度量极限。已经建立了各种族与不同作者报告的解之间的关系。在具有宇宙常数的解类中，占据重要位置的是：静电和磁静的Peldan解，静态均匀和旋转的Clement类，具有特定Kamata-Koikawa解的常电磁不变量分支，混合循环对称静态黑洞场，以及通过$SL(2,R)$变换生成的同样重要的解，其中包括Clement旋转带电解，Martinez-Teitelboim-Zanelli黑洞解和Dias-Lemos度量值得提及。 显示英文摘要

摘要： From a general metric for stationary cyclic symmetric gravitational fields coupled to Maxwell electromagnetic fields within the $(2+1)$-dimensional gravity the uniqueness of wide families of exact solutions is established, among them, all uniform electromagnetic solutions possessing electromagnetic fields with vanishing covariant derivatives, all fields having constant electromagnetic invariants $F_{\mu\nu}\,F^{\mu\nu}$ and $T_{\mu\nu}\,T^{\mu\nu}$, the whole classes of hybrid electromagnetic solutions, and also wide classes of stationary solutions are derived for a third order nonlinear key equations. Certain of these families can be thought of as black hole solutions. For the most general set of Einstein-Maxwell equations, reducible to three non-linear equations for the three unknown functions, two new classes of solutions-having anti-de Sitter spinning metric limit-are derived. The relationship of various families with those reported by different authors' solutions has been established. Among the classes of solutions with cosmological constant a relevant place occupy: the electrostatic and magnetostatic Peldan solutions, the stationary uniform and spinning Clement classes, the constant electromagnetic invariant branches with the particular Kamata-Koikawa solution, the hybrid cyclic symmetric stationary black hole fields, and the non-less important solutions generated via $SL(2,R)$ transformations where the Clement spinning charged solution, the Martinez-Teitelboim-Zanelli black hole solution, and Dias-Lemos metric merit mention.