标题： 奇点极限之前的普遍宇宙学解的几何学 显示英文标题

标题： Geometry of the generical cosmological solution before the singularity limit

摘要： 对通用宇宙学解的分析既针对到宇宙奇点的非渐近极限，也针对其渐近极限进行解析。 Bianchi I 解和 Bichani IX 解被描述为一系列重新参数化的 Bianchi I 解，并根据度规张量的空间部分所暗示的渐近对称性进行了分析。 数值研究得到了解释。 通过利用爱因斯坦场方程初始条件的自由度，即那些不一定属于 Bichani 模型的自由度，提出了半经典区域。 讨论并应用了适用于通用偏微分方程系统的适当同质化技术和去同质化技术，这些技术与包含与哈密顿约束解相关哈密顿问题动力学的仿射（Misner）空间有关。 对于通用宇宙学解到宇宙奇点的渐近极限，在 BKL 方法的渐近 Kasner 参数化以及 Misner-Chitre 形式中得以实现。 在 Misner-Chitre 方法中，EFE 对非渐近自由度施加了限制，这使得能够在各向异性平面上定义解的类别。 显示英文摘要

摘要： The generic cosmological solution is analyzed both for the non-asymptotic limit to the cosmological singularity and in the asymptotic limit analytically. The Bianchi I solution and the Bianchi IX solution, described as a sequence of Bianchi I reparameterized solutions, are analyzed with respect to the asymptotic symmetry implied by the space part of the metric tensor. Numerical studies are explained. The semiclassical regime is proposed by using the degrees of freedom for the initial conditions to the Einstein field equations, i.e. those which are not necessarily characterizing for a Bianchi scheme. The appropriate homegeneization techniques and the de-homogenization techniques referred to a generic system of PDE's are discussed and applied to the affine (Misner) space containing the dynamics pertinent to the Hamiltonian problem associated to the solution of the Hamiltonian constraint. The asymptotic limit to the cosmological singularity for the generic cosmological solution is implemented within the asymptotic Kasner parametrization of the BKL approach and for the Misner-Chitre formalism. The EFE in the Misner-Chitre approach imply constraints on the non-asymptotical degrees of freedom, which allow one to define classes of solutions on the anisotropy plane.