引力场中的参变非完整标架变换及其精确解
Parametric Nonholonomic Frame Transforms and Exact Solutions in Gravity
摘要：
给出了构造爱因斯坦理论及其推广中引力场方程精确解的一种广义几何方法。首先，我们应用非完整框架变形的形式主义（正式考虑非完整流形和Finsler空间）时，引力场方程转化为非线性偏微分方程组，可以在一般形式的集成。如果我们考虑四维（或五维）时空，则新的解类由取决于一个、两个和三个（或三个和四个）变量的积分函数的通用非对角度量定义。其次，我们使用一个一般的计划时，一个（两个）参数族的精确解定义的任何源自由的解决方案的爱因斯坦方程与一个（两个）Killing向量场（S）。一个连续的迭代过程的结果在一类新的解决方案，其特征在于无限多个参数的非阿贝尔群涉及任意函数的一个变量。在真空爱因斯坦和弦引力中构造了五类描述孤子pp波相互作用的非对角精确解。我们探讨可能的物理后果，这些解决方案来自主要史瓦西或PP波度量。
英文摘要：
A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for nonholonomic manifolds and Finsler spaces) when the gravitational field equations transform into systems of nonlinear partial differential equations which can be integrated in general form. The new classes of solutions are defined by generic off-diagonal metrics depending on integration functions on one, two and three (or three and four) variables if we consider four (or five) dimensional spacetimes. Second, we use a general scheme when one (two) parameter families of exact solutions are defined by any source-free solutions of Einstein's equations with one (two) Killing vector field(s). A successive iteration procedure results in new classes of solutions characterized by an infinite number of parameters for a non-Abelian group involving arbitrary functions on one variable. Five classes of exact off-diagonal solutions are constructed in vacuum Einstein and in string gravity describing solitonic pp-wave interactions. We explore possible physical consequences of such solutions derived from primary Schwarzschild or pp-wave metrics.
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