奇异的或失败的强宇宙审查在四维空间
Exotica or the failure of the strong cosmic censorship in four dimensions
摘要：
在这封信中，一个通用的反例强宇宙审查员猜想展出。更准确地说-考虑到该猜想缺乏任何精确的公式，但-首先，我们有意义的是什么意思的“一般反例”，通过引入数学上明确和逻辑上更强的概念“强大的反例”。然后利用彭罗斯的非线性引力子结构（即，扭量理论）和Wick旋转技巧，我们在Gompf-Taubes不可数径向大奇异族${\mathbb R}^4$的最大成员上构造了一个光滑的Ricci平坦但不平坦的Lorentz度规.我们观察到，这种解决方案的洛伦兹真空爱因斯坦方程消失的宇宙学常数为我们提供了一种反例，这是弱于一个“强大的反例”，但仍然是合理的考虑作为一个“一般的反例”。有趣的是，这种反例只存在于四维空间中。
英文摘要：
In this letter a generic counterexample to the strong cosmic censor conjecture is exhibited. More precisely---taking into account that the conjecture lacks any precise formulation yet---first we make sense of what one would mean by a "generic counterexample" by introducing the mathematically unambigous and logically stronger concept of a "robust counterexample". Then making use of Penrose' nonlinear graviton construction (i.e., twistor theory) and a Wick rotation trick we construct a smooth Ricci-flat but not flat Lorentzian metric on the largest member of the Gompf--Taubes uncountable radial family of large exotic ${\mathbb R}^4$'s. We observe that this solution of the Lorentzian vacuum Einstein's equations with vanishing cosmological constant provides us with a sort of counterexample which is weaker than a "robust counterexample" but still reasonable to consider as a "generic counterexample". It is interesting that this kind of counterexample exists only in four dimensions.
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