标题： Kasner-like奇点的局部构造 显示英文标题

标题： A localized construction of Kasner-like singularities

摘要： 我们构建了时空局部的奇异解，这些解在过去的边界上表现出类似Kasner的行为。 我们的结果可以看作是\cite{FL}中构造的局部化（在空间上）。 我们还证明了一个改进的唯一性陈述，并给出一个简单的论证，生成类似Kasner的奇点的一般渐近数据，享有所有预期的自由度，尽管仅在空间局部范围内。 与\cite{FL}相比，本工作的关键区别在于我们使用了一种一阶对称双曲形式的真空爱因斯坦方程，相对于与高斯时间叶层适应的平行传播正交标架的连接系数。 这使得构造更容易局部化，因为不再需要椭圆估计来完成能量论证。 显示英文摘要

摘要： We construct local, in spacetime, singular solutions to the Einstein vacuum equations that exhibit Kasner-like behavior in their past boundary. Our result can be viewed as a localization (in space) of the construction in \cite{FL}. We also prove a refined uniqueness statement and give a simple argument that generates general asymptotic data for Kasner-like singularities, enjoying all expected degrees of freedom, albeit only locally in space. The key difference of the present work with \cite{FL} is our use of a first order symmetric hyperbolic formulation of the Einstein vacuum equations, relative to the connection coefficients of a parallelly propagated orthonormal frame which is adapted to the Gaussian time foliation. This makes it easier to localize the construction, since elliptic estimates are no longer required to complete the energy argument.