广义相对论、劳里切拉超几何函数$F_D$和辫子理论
General relativity, Lauricella's hypergeometric function $F_D$ and the theory of braids
摘要：
描述Kerr和Kerr-（anti）de Sitter时空中试验粒子和光子运动的广义相对论运动方程的精确（封闭）解都涉及Lauricella $F_D$：Kraniotis [Class.量子重力{ \bf 21} 2004，4743; Class.量子重力{ \bf 22} 2005，4391; Class.量子重力{ \bf 24} 2007，1775]。相应函数的变量域${\cal D}_n$取决于与克尔-（反）德西特度规和卡特常数$Q$的等距相关的第一运动积分，以及宇宙学常数$Λ$和克尔（旋转）参数。在这项工作中，我们讨论的域${\cal D}_n$的拓扑性质，特别是它的基本连接与理论的辫子。建立了广义相对论与纯辫子的内在联系。
英文摘要：
The exact (closed form) solutions of the equations of motion in the theory of general relativity that describe motion of test particle and photon in Kerr and Kerr-(anti) de Sitter spacetimes all involve the multivariable hypergeometric function of Lauricella $F_D$: Kraniotis [Class. Quantum Grav. {\bf 21} 2004, 4743; Class. Quantum Grav. {\bf 22} 2005, 4391; Class. Quantum Grav. {\bf 24} 2007, 1775]. The domain of variables ${\cal D}_n$ of the corresponding function depends on the first integrals of motion associated with the isometries of the Kerr-(anti) de Sitter metric and Carter's constant $Q$ as well as on the cosmological constant $Λ$ and the Kerr (rotation) parameter. In this work we discuss the topological properties of the domain ${\cal D}_n$ and in particular its fundamental connection with the theory of braids. An intrinsic relationship of general relativity with the pure braids is established.
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