广义相对论中的完整性奇点与时空的$C^{0,1}_{\mathrm{loc}}$ -不可拓性
On holonomy singularities in general relativity and the $C^{0,1}_{\mathrm{loc}}$-inextendibility of spacetimes
摘要：
本文在联系的层次上研究引力奇点的结构。我们特别表明，FLRW时空与粒子视界的局部holonomy，这是相关的引力能，成为无界附近的大爆炸奇点。这意味着这种FLRW时空的$C^{0,1}_{\mathrm{loc}}$ -不可扩展性。再次使用无界局部完整性，我们也给出了一个一般定理，建立$C^{0,1}_{\mathrm{loc}}$ -不可扩展的球对称弱零奇点出现在柯西视界的内部黑洞。我们的定理并不以质量暴胀为前提，特别适用于Reissner-Nordström-Vaidya时空，也适用于Einstein-Maxwell-标量场系统的两端次极值Reissner-Nordström初始数据的一般球对称小扰动所产生的时空。在[26]中，[27] Luk和Oh证明了$C^2$ -后一类时空的强宇宙监督的公式-并且基于他们的工作，我们将其改进为强宇宙监督的$C^{0,1}_{\mathrm{loc}}$公式。
英文摘要：
This paper investigates the structure of gravitational singularities at the level of the connection. We show in particular that for FLRW spacetimes with particle horizons a local holonomy, which is related to a gravitational energy, becomes unbounded near the big-bang singularity. This implies the $C^{0,1}_{\mathrm{loc}}$-inextendibility of such FLRW spacetimes. Again using an unbounded local holonomy we also give a general theorem establishing the $C^{0,1}_{\mathrm{loc}}$-inextendibility of spherically symmetric weak null singularities which arise at the Cauchy horizon in the interior of black holes. Our theorem does not presuppose the mass-inflation scenario and in particular applies to the Reissner-Nordström-Vaidya spacetimes as well as to spacetimes which arise from small and generic spherically symmetric perturbations of two-ended subextremal Reissner-Nordström initial data for the Einstein-Maxwell-scalar field system. In [26], [27] Luk and Oh proved the $C^2$-formulation of strong cosmic censorship for this latter class of spacetimes -- and based on their work we improve this to a $C^{0,1}_{\mathrm{loc}}$-formulation of strong cosmic censorship.
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