论文标题
短脉冲数据的黑洞形成的渐近描述
Asymptotic description of the formation of black holes from short-pulse data
论文作者
论文摘要
在这篇论文中，我们介绍了从克里斯托杜乌（Christodoulou）的短脉冲安萨兹（Ansatz）的四维爱因斯坦真空方程中黑洞动态形成的部分进步。我们在推定的溶液指标中识别自然缩放率，并使用真实爆炸的技术提出了一个垂直的歧管和相关的重新缩放切线束（我们称为“短脉冲切线束”），该捆绑包在该捆绑包上是规则的。我们证明了在爆炸歧管的每个边界面上正式求解真空爱因斯坦方程的解决方案的存在，并表明，对于一组开放的限制性短脉冲数据，正式溶液在desingulinalizatizalized歧管的边界高度外面的一个hypersurface上表现出曲率爆炸。 该论文旨在部分说明。特别是，本文提出了双记号仪表的解释，以及爱因斯坦方程的特征初始价值问题的解决方案，以及对克里斯托杜洛（Christodoulou）在捕获表面动态形成的纪念性结果的新观点的阐述。
In this thesis we present partial progress towards the dynamic formation of black holes in the four-dimensional Einstein vacuum equations from Christodoulou's short-pulse ansatz. We identify natural scaling in a putative solution metric and use the technique of real blowup to propose a desingularized manifold and an associated rescaled tangent bundle (which we call the "short-pulse tangent bundle") on which the putative solution remains regular. We prove the existence of a solution solving the vacuum Einstein equations formally at each boundary face of the blown-up manifold and show that for an open set of restricted short-pulse data, the formal solution exhibits curvature blowup at a hypersurface in one of the boundary hypersurfaces of the desingularized manifold. This thesis is intended to be partially expository. In particular, this thesis presents an exposition of double-null gauges and the solution of the characteristic initial value problem for the Einstein equations, as well as an exposition of a new perspective of Christodoulou's monumental result on the dynamic formation of trapped surfaces.
