Naked singularities for the Einstein vacuum equations: The exterior solution

• 成果类型: Article
• 署名作者: Rodnianski, Igor; Shlapentokh-Rothman, Yakov
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2023.198.1.3
• 发表日期: 2023
• 页码: 231-391
• 关键词: initial-value problem; gravitational collapse; cosmic censorship; STABILITY; EXISTENCE; Examples

摘要

In this work we initiate the mathematical study of naked singularities for the Einstein vacuum equations in 3 + 1 dimensions by constructing solutions which correspond to the exterior region of a naked singularity. A key element is our introduction of a new type of self-similarity for the Einstein vacuum equations. Connected to this is a new geometric twisting phenomenon which plays the leading role in singularity formation.Prior to this work, the only known examples of naked singularities were the solutions constructed by Christodoulou for the spherically symmetric Einstein-scalar-field system, as well as other solutions explored numerically for either the spherically symmetric Einstein equations coupled to suitable matter models or for the Einstein equations in higher dimensions.