Einstein-Euler系统中的裸奇点

IF 2.4 1区 数学 Q1 MATHEMATICS Annals of Pde Pub Date : 2023-02-07 DOI:10.1007/s40818-022-00144-3
Yan Guo, Mahir Hadzic, Juhi Jang
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引用次数: 4

摘要

1990年,基于数值和形式渐近分析,Ori和Piran预测了自相似时空的存在,称为相对论性Larson-Penston解,这些自相似时空可以被适当地压平,以从光滑的初始数据中获得动态形成裸奇点的时空示例,并求解径向对称的Einstein-Euler系统。尽管它很重要,但对这种时空存在的严格证明仍然难以捉摸,部分原因是在所谓的音速超表面上进行分析的复杂性。我们提供了严格的数学证明。我们的策略基于对与底层非自治动力系统相关的非线性不变量的精细研究,该问题在自相似约简后被约简为该系统。关键的技术成分是为该问题量身定制的单调性引理,为构建将音速超曲面连接到所谓的弗里德曼解的解而开发的特设射击方法,以及为构建解的最大解析扩展而开发的非线性论点。最后,我们在双零规范中重新表述问题,使自相似轮廓变平,从而获得具有孤立裸奇异性的渐近平坦时空。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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Naked Singularities in the Einstein-Euler System

In 1990, based on numerical and formal asymptotic analysis, Ori and Piran predicted the existence of selfsimilar spacetimes, called relativistic Larson-Penston solutions, that can be suitably flattened to obtain examples of spacetimes that dynamically form naked singularities from smooth initial data, and solve the radially symmetric Einstein-Euler system. Despite its importance, a rigorous proof of the existence of such spacetimes has remained elusive, in part due to the complications associated with the analysis across the so-called sonic hypersurface. We provide a rigorous mathematical proof. Our strategy is based on a delicate study of nonlinear invariances associated with the underlying non-autonomous dynamical system to which the problem reduces after a selfsimilar reduction. Key technical ingredients are a monotonicity lemma tailored to the problem, an ad hoc shooting method developed to construct a solution connecting the sonic hypersurface to the so-called Friedmann solution, and a nonlinear argument to construct the maximal analytic extension of the solution. Finally, we reformulate the problem in double-null gauge to flatten the selfsimilar profile and thus obtain an asymptotically flat spacetime with an isolated naked singularity.

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来源期刊
Annals of Pde
Annals of Pde Mathematics-Geometry and Topology
CiteScore
3.70
自引率
3.60%
发文量
22
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