标题： 动力学真空黑洞的内部 I：Kerr 时序奇点的$C^0$稳定性 显示英文标题

标题： The interior of dynamical vacuum black holes I: The $C^0$-stability of the Kerr Cauchy horizon

摘要： 我们开始一系列研究，探讨没有对称性的动力学旋转真空黑洞的内部。 在本文中，我们从爱因斯坦真空方程在黑洞内部已处于事件视界内的超曲面上定义的适当柯西数据出发，来研究这个问题，这些数据代表了预期的几何结构，即事件视界内部的几何结构。 我们证明，对于所有这样的数据，最大柯西演化可以扩展到一个非平凡的柯西视界部分，作为一个具有连续度规的洛伦兹流形。 在后续工作中，我们将重新审视我们的数据假设，仅假设黑洞事件视界的几何结构适当渐近于一个旋转的克尔解。 特别是，如果克尔族的外部区域被证明是动态稳定的——这是广泛预期的——那么将得出结论，彭罗斯著名的强宇宙审查猜想的$C^0$-不可延拓性表述实际上是错误的。 然而，证明表明，由此产生的$C^0$-度规柯西视界在本质上通常是奇异的，代表所谓的“弱零奇点”，因此，强宇宙审查猜想的一个修正版本是成立的。 显示英文摘要

摘要： We initiate a series of works where we study the interior of dynamical rotating vacuum black holes without symmetry. In the present paper, we take up the problem starting from appropriate Cauchy data for the Einstein vacuum equations defined on a hypersurface already within the black hole interior, representing the expected geometry just inside the event horizon. We prove that for all such data, the maximal Cauchy evolution can be extended across a non-trivial piece of Cauchy horizon as a Lorentzian manifold with continuous metric. In subsequent work, we will retrieve our assumptions on data assuming only that the black hole event horizon geometry suitably asymptotes to a rotating Kerr solution. In particular, if the exterior region of the Kerr family is proven to be dynamically stable---as is widely expected---then it will follow that the $C^0$-inextendibility formulation of Penrose's celebrated strong cosmic censorship conjecture is in fact false. The proof suggests, however, that the $C^0$-metric Cauchy horizons thus arising are generically singular in an essential way, representing so-called "weak null singularities", and thus that a revised version of strong cosmic censorship holds.