论文标题
解决方案将方法作为解决方案空间中的“坐标”转换
Solution generating methods as "coordinate" transformations in the solution spaces
论文作者
论文摘要
较早发现的解决方案生成的方法是针对爱因斯坦和爱因斯坦 - 麦克斯韦现场方程（例如孤子生成技术，b $ \ ddot {a} $ cklund或对称转换和其他组理论方法）的跨度sque sque sorecations sorections的变换。通常，可以通过相应频谱问题的基本解决方案的单片数据来执行此类“坐标”的作用。但是，对于大型田地子类，这些可能是由时空等轴测组的这种变性轨道组成的边界上的Ernst势值的值，在该范围内，时空的几何形状和电磁场具有正常的行为。在本文中，这种“坐标”的转换，与不同的已知解决方案生成过程相对应的相对应的代数表达式不需要任何特定选择的初始（背景）解决方案来描述。这些转换的明确形式使我们能够在不同解决方案生成过程中出现的自由参数集之间找到相互关系，并在其所有组件的详细计算之前，都可以确定每个生成解决方案的某些物理和几何属性。
The solution generating methods discovered earlier for integrable reductions of Einstein's and Einstein - Maxwell field equations (such as soliton generating techniques, B$\ddot{a}$cklund or symmetry transformations and other group-theoretical methods) can be described explicitly as transformations of especially defined "coordinates" in the infinite-dimensional solution spaces of these equations. In general, the role of such "coordi\-nates", which characterize every local solution, can be performed by the monodromy data of the fundamental solutions of the corresponding spectral problems. However for large subclasses of fields, these can be the values of the Ernst potentials on the boundaries which consist of such degenerate orbits of the space-time isometry group, in which neighbourhood the space-time geometry and electromagnetic fields possess a regular behaviour. In this paper, transformations of such "coordinates", corresponding to different known solution generating procedures are described by simple enough algebraic expressions which do not need any particular choice of the initial (background) solution. Explicit forms of these transformations allow us to find the interrelations between the sets of free parameters, which arise in different solution generating procedures, as well as to determine some physical and geometrical properties of each generating solution even before a detail calculations of all its components.
