论文标题
真空中崩溃的空间的构造
A construction of collapsing spacetimes in vacuum
论文作者
论文摘要
在本文中，我们在没有任何对称性的情况下在真空中构建了一类崩溃的空间。时空包含一个黑洞区域，该区域与未来的事件视野从过去界定。它具有cauchy hyperface，其琐碎拓扑位于黑洞区域之外。基于文献中现有的技术，可以原则上的时空构造为过去的地质完整和渐近地对Minkowski空间。该结构基于真空爱因斯坦方程的半全球存在结果，该方程建立在Christodoulou最初在其作品中的作品中建立的A先验估计的修改版本，并在陷阱表面形成方面，以及在黑洞内进行的粘合结构。特别是，提供了存在所需的先验估计值的完整细节，这可以看作是Christodoulou原始论点的简化。
In this paper, we construct a class of collapsing spacetimes in vacuum without any symmetries. The spacetime contains a black hole region which is bounded from the past by the future event horizon. It possesses a Cauchy hypersurface with trivial topology which is located outside the black hole region. Based on existing techniques in the literature, the spacetime can in principle be constructed to be past geodesically complete and asymptotic to Minkowski space. The construction is based on a semi-global existence result of the vacuum Einstein equations built on a modified version of the a priori estimates that were originally established by Christodoulou in his work on the formation of trapped surface, and a gluing construction carried out inside the black hole. In particular, the full detail of the a priori estimates needed for the existence is provided, which can be regarded as a simplification of Christodoulou's original argument.
