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arXiv 2304.04444gr-qcmath.APmath.DG
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具有有界曲率的强宇宙审查

Strong Cosmic Censorship with Bounded Curvature

Moritz Reintjes

AI总结:

本文提出了一个较弱的强宇宙审查(SCC)猜想版本,要求最大Cauchy发展无法被具有Lipschitz连续度量和$L^p$有界曲率的流形延拓,并在假设无更高联络正则性延拓的前提下,证明了对足够大的$p$该猜想成立。

摘要:

在本文中,我们提出了Penrose备受关注的强宇宙审查(SCC)猜想的一个较弱版本,断言最大Cauchy发展无法通过具有Lipschitz连续Lorentzian度量且Riemann曲率在$L^p$中有界的流形进行延拓。Lipschitz连续性是因果结构的阈值正则性,而曲率界排除了无限潮汐加速度,这论证了该较弱SCC猜想的物理意义。本文的主要结果在假设不存在具有更高联络正则性$W^{1,p}_\ ext{loc}$的延拓的前提下,肯定地证明了对于足够大的$p$(有均匀界时$p>4$,无均匀界时$p>2$),该具有有界曲率的SCC猜想成立。

英文摘要:

In this paper we propose a weaker version of Penrose's much heeded Strong Cosmic Censorship (SCC) conjecture, asserting inextentability of maximal Cauchy developments by manifolds with Lipschitz continuous Lorentzian metrics and Riemann curvature bounded in $L^p$. Lipschitz continuity is the threshold regularity for causal structures, and curvature bounds rule out infinite tidal accelerations, arguing for physical significance of this weaker SCC conjecture. The main result of this paper, under the assumption that no extensions exist with higher connection regularity $W^{1,p}_\text{loc}$, proves in the affirmative this SCC conjecture with bounded curvature for $p$ sufficiently large, ($p>4$ with uniform bounds, $p>2$ without uniform bounds).

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。

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