Let $M$ be a connected, simply connected, oriented, closed, smooth four-manifold which is spin (or equivalently having even intersection form) and put $M^{\times }≔M\setminus \left\{\mathrm{point}\right\}$. In this paper we prove that if $X^{\times }$ is a smooth four-manifold homeomorphic but not necessarily diffeomorphic to $M^{\times }$ (more precisely, it carries a smooth structure à la Gompf) then $X^{\times }$ can be equipped with a complete Ricci-flat Riemannian metric. As a byproduct of the construction it follows that this metric is self-dual as well consequently $X^{\times }$ with this metric is in fact a hyper-Kähler manifold. In particular we find that the largest member of the Gompf–Taubes radial family of large exotic ${\mathbb{R}}^4$’s admits a complete Ricci-flat metric (and in fact it is a hyper-Kähler manifold).

These Riemannian solutions are then converted into Ricci-flat Lorentzian ones thereby exhibiting lot of new vacuum solutions which are not accessible by the initial value formulation. A natural physical interpretation of them in the context of the strong cosmic censorship conjecture and topology change is discussed.

让 $\mathrm{中号}$ 是一个连接的，简单连接的，定向的，闭合的，光滑的四歧管，该四歧管旋转（或等效地具有偶数相交形式）并放置 ${\mathrm{中号}}^{\times }≔\mathrm{中号}\setminus \left\{\mathrm{观点}\right\}$。在本文中，我们证明$X^{\times }$ 是光滑的四流形同胚，但不一定对 ${\mathrm{中号}}^{\times }$（更确切地说，它带有一个光滑结构点菜Gompf）然后$X^{\times }$可以配备完整的Ricci-flat Riemannian度量。作为构造的副产品，因此该度量标准也是自对偶的$X^{\times }$使用此度量标准实际上是超凯勒流形。特别是，我们发现Gompf–Taubes径向异域家族的最大成员${\mathbb{[R}}^4$承认了完整的Ricci-flat指标（实际上，它是一个超Kähler流形）。

然后，将这些黎曼解决方案转换为Ricci-flat Lorentzian解决方案，从而展示出许多新的真空解决方案，这些价值无法通过初始值公式获得。讨论了在强大的宇宙检查猜想和拓扑变化的背景下对它们的自然物理解释。