论文标题
关于一般相对论和$ c^{0,1} _ {\ mathrm {loc}} $的$ c^{0,1} $ - 空位的不可超时性
On holonomy singularities in general relativity and the $C^{0,1}_{\mathrm{loc}}$-inextendibility of spacetimes
论文作者
论文摘要
本文研究了连接级别的重力奇异性的结构。我们特别表明，对于用粒子范围的FLRW空间，与重力能量有关的局部单位物在大键奇点附近无限。这意味着$ c^{0,1} _ {\ mathrm {loc}} $ - 这种flrw spacetimes的不可扩展性。再次使用无限的局部固体，我们还提供了一个一般定理，以建立$ c^{0,1} _ {\ mathrm {loc}} $ - 在黑色孔内部的凯奇（Cauchy）地平线上出现的球形对称弱的无效的无效无效的无效无效的奇异性。我们的定理并未以质量流动的情况为前提，尤其适用于Reissner-Nordström-Vaidya SpaceTimes，以及空位，这些空间是由两端端超级超级Reissner-Reissner-Reissner-Reissner-NordströmMaxeN-Maxein-Maxein-Maxein-Maxein-Maxel-Scalarar field Systems的小型球形对称性扰动引起的。在[26]，[27]中，卢克和哦，证明了$ c^2 $ - 对后一类的空间进行强宇宙审查制度 - 基于他们的工作，我们将其改进到$ c^{0,1} _ {\ mathrm {loc}}} $ - 强大的宇宙审查的形式。
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.
