Naked singularities for the Einstein vacuum equations: The exterior solution
Naked singularities for the Einstein vacuum equations: The exterior solution
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DOI：
10.4007/annals.2023.198.1.3
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发表时间：
2019-12
影响因子：
4.9
通讯作者：
I. Rodnianski;Yakov Shlapentokh-Rothman
中科院分区：
文献类型：
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作者：
I. Rodnianski;Yakov Shlapentokh-Rothman
在这项工作中，我们通过构造对应于裸奇点外部区域的解，开始了3+1维度爱因斯坦真空方程裸奇点的数学研究。一个关键因素是我们为爱因斯坦真空方程引入了一种新的自相似性。与此相关的是一种新的几何扭曲现象，它在奇点的形成中起主导作用。在这项工作之前，已知的裸奇点的唯一例子是Christodoulou为球对称爱因斯坦-标量场系统构造的解，以及其他对球对称爱因斯坦方程耦合到合适的物质模型或更高维度的爱因斯坦方程进行数值探索的解。
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.