标题： "变量分离与厄恩斯特方程的哈密顿形式" 显示英文标题

标题： "Separation of Variables and Hamiltonian Formulation for the Ernst Equation"

摘要： 证明了对于任意的静态轴对称时空，真空爱因斯坦方程可以通过将厄恩斯坦方程及其相关的线性系统重新表述为一个非自治的施莱辛格型动力系统而完全分离。 度规的共形因子在存在有限多个正则奇点的情况下，与厄恩斯坦方程的$\tau$函数相吻合（最多相差一个显式可计算的因子）。 我们还给出了这些结果的一个规范形式，该形式基于一种“双时间”哈密顿方法，并为这类系统的量子化开辟了新的途径。 显示英文摘要

摘要： It is shown that the vacuum Einstein equations for an arbitrary stationary axisymmetric space-time can be completely separated by re-formulating the Ernst equation and its associated linear system in terms of a non-autonomous Schlesinger-type dynamical system. The conformal factor of the metric coincides (up to some explicitly computable factor) with the $\tau$-function of the Ernst equation in the presence of finitely many regular singularities. We also present a canonical formulation of these results, which is based on a ``two-time" Hamiltonian approach, and which opens new avenues for the quantization of such systems.