由短脉冲数据对黑洞形成的渐近描述
Asymptotic description of the formation of black holes from short-pulse data
摘要：
在这篇论文中，我们介绍了从Christodoulou的短脉冲实验中得到的四维爱因斯坦真空方程中黑洞的动力学形成的部分进展。我们确定自然缩放在一个假定的解决方案度量，并使用真正的爆破技术，提出一个desingularized流形和相关的重新缩放的切丛（我们称之为“短脉冲切丛“）上的假定的解决方案保持定期。我们证明了一个解决方案的存在性，正式解决真空爱因斯坦方程的爆破流形的每个边界面，并表明，对于一个开放的一组限制短脉冲数据，形式解表现出曲率爆破在超曲面中的一个边界超曲面的desingularized流形。本论文的目的是部分说明。特别是，本论文提出了一个双零规范和爱因斯坦方程的特征初值问题的解决方案的阐述，以及阐述了一个新的角度Christodoulou的不朽成果的动态形成的陷阱表面。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
