一类可积函数
A Class of Integrable Metrics
摘要：
在四维空间中，允许两个Killing向量和一个秩为2的Killing张量的最一般度量可以由一个变量的十个任意函数参数化。我们发现，挑选一个特殊的vierbien，减少系统的8个功能，意味着存在两个测地线和共享免费，零同余，产生的两个主要零方向的Weyl张量。因此，如果时空是一个爱因斯坦流形，戈德堡-萨克斯定理意味着它是彼得罗夫D型，并且通过明确的构造，它是卡特类。因此，我们的分析提供了最一般的可积结构和卡特时空家族之间的直接联系。
英文摘要：
In four dimensions, the most general metric admitting two Killing vectors and a rank-two Killing tensor can be parameterized by ten arbitrary functions of a single variable. We show that picking a special vierbien, reducing the system to eight functions, implies the existence of two geodesic and share-free, null congruences, generated by two principal null directions of the Weyl tensor. Thus, if the spacetime is an Einstein manifold, the Goldberg-Sachs theorem implies it is Petrov type D, and by explicit construction, is in the Carter class. Hence, our analysis provide an straightforward connection between the most general integrable structure and the Carter family of spacetimes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
