标题： 雷斯纳-诺德斯特罗姆时空在引力的四维规范理论中 显示英文标题

标题： Reissner-Nordström Spacetime in the Tetrad Theory of Gravitation

摘要： 我们给出了在四维引力理论中带有带电源的耦合引力和电磁场的球对称精确解的两类解。 第一个解依赖于一个任意函数$H({R},t)$。 第二个解依赖于一个常数参数$\eta$。 这些解产生相同的度规，即Reissner--Nordstr$\ddot{o}$度规。 如果表征第一个解的任意函数和第二个解的任意常数被设为零，那么这两个精确解将彼此重合。 然后我们使用超势方法计算与这些解析解相关的能量含量。 特别是，我们检查这些解是否满足M{\o }ller 对一致能量动量复数所要求的条件：即检查孤立系统的总四动量在洛伦兹变换下是否表现出四矢量的行为。 随后发现，任意函数应比$1/\sqrt{R}$更快地衰减，对于$R\to \infty$而言。 还表明第二个精确解满足M{\o }ller 的条件。 显示英文摘要

摘要： We give two classes of spherically symmetric exact solutions of the couple gravitational and electromagnetic fields with charged source in the tetrad theory of gravitation. The first solution depends on an arbitrary function $H({R},t)$. The second solution depends on a constant parameter $\eta$. These solutions reproduce the same metric, i.e., the Reissner--Nordstr$\ddot{o}$m metric. If the arbitrary function which characterizes the first solution and the arbitrary constant of the second solution are set to be zero, then the two exact solutions will coincide with each other. We then calculate the energy content associated with these analytic solutions using the superpotential method. In particular, we examine whether these solutions meet the condition which M{\o}ller required for a consistent energy-momentum complex: Namely, we check whether the total four-momentum of an isolated system behaves as a four-vector under Lorentz transformations. It is then found that the arbitrary function should decrease faster than $1/\sqrt{R}$ for $R\to \infty$. It is also shown that the second exact solution meets the M{\o}ller's condition.