# Global solvability of the vacuum Einstein equation and the strong cosmic censor conjecture in four dimensions

11 Sep 2020 Etesi Gabor

Let $M$ be a connected, simply connected, oriented, closed, smooth four-manifold which is spin (or equivalently having even intersection form) and put $M^\times:=M\setminus\{{\rm point}\}$.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 {\it \`a 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-K\"ahler manifold... (read more)

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• DIFFERENTIAL GEOMETRY
• GENERAL RELATIVITY AND QUANTUM COSMOLOGY