论文标题
爱因斯坦真空方程的裸奇异点：内部解决方案
Naked Singularities for the Einstein Vacuum Equations: The Interior Solution
论文作者
论文摘要
在先前的工作中[I。 Rodnianski和Y. Shlapentokh-Rothman，爱因斯坦真空方程的裸奇异物：外部解决方案，Arxiv：1912.08478]，我们在3+1个维度的Einstein真空方程式中构建了解决方案，这些方程与裸露的单个裸露的象征性区域相对应。在这项工作中，我们构建了与内部区域相对应的溶液，并表明这两种溶液可以粘合在一起以产生赤裸的奇异性。我们构造的基础是我们在以前的工作中引入的爱因斯坦真空方程的新型自相似性，也是对新型的quasilinear PDE的研究。
In a previous work [I. Rodnianski and Y. Shlapentokh-Rothman, Naked Singularities for the Einstein Vacuum Equations: The Exterior Solution, arXiv:1912.08478] we constructed solutions to the Einstein vacuum equations in 3+1 dimensions which corresponded to the exterior region of a naked singularity. In this work we construct solutions which correspond to the interior region and show that the two solutions may be glued together to produce a naked singularity. Fundamental to our construction is the novel type of self-similarity for the Einstein vacuum equations that we introduced in our previous work and also the study of a new class of quasilinear PDE's of mixed degenerate elliptic-hyperbolic type.
