Alekseev GA, Griffiths JB
Steklov Mathematical Institute, Gubkina 8, Moscow 117966, GSP-1, Moscow, Russia.
Phys Rev Lett. 2000 Jun 5;84(23):5247-50. doi: 10.1103/PhysRevLett.84.5247.
For space-times with two spacelike isometries, we present infinite hierarchies of exact solutions of the Einstein and Einstein-Maxwell equations as represented by their Ernst potentials. This hierarchy contains three arbitrary rational functions of an auxiliary complex parameter. They are constructed using the so-called "monodromy transform" approach and our new method for the solution of the linear singular integral equation form of the reduced Einstein equations. The solutions presented, which describe inhomogeneous cosmological models or gravitational and electromagnetic waves and their interactions, include a number of important known solutions as particular cases.
对于具有两个类空等距性的时空，我们给出了由其恩斯特势表示的爱因斯坦方程和爱因斯坦 - 麦克斯韦方程的无穷精确解族。这个解族包含一个辅助复参数的三个任意有理函数。它们是使用所谓的“单值性变换”方法以及我们求解简化爱因斯坦方程的线性奇异积分方程形式的新方法构建的。所给出的解描述了非均匀宇宙学模型或引力波和电磁波及其相互作用，其中包括许多重要的已知解作为特殊情况。
