2019/03/31 by Gabor Etesi, Gábor Etesi
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Conjecture #Context (archaeology) #Cosmic censorship hypothesis #Diffeomorphism #Einstein #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Holonomy #Manifold (fluid mechanics) #Mathematical physics #Mathematics #Metric (unit) #Pure mathematics #Ricci curvature #Riemannian manifold #gr-qc #math.DG
paper · pdf · doi:10.1016/j.geomphys.2021.104164
published as Journ. Geom. Phys. 164, 104164, 21 pp. (2021) · LaTeX, 31 pp., 7 figures; this is the final published version based on our earlier works on arXiv:1503.04945, arXiv:1707.09180 and arXiv:1905.03952
openalex publication_date 2021/02/11 · arxiv created 2021/03/02 · arxiv updated 2021/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Let M be a connected, simply connected, oriented, closed, smooth four-manifold which is spin (or equivalently having even intersection form) and put M×≔M∖point. In this paper we prove that if X× is a smooth four-manifold homeomorphic but not necessarily diffeomorphic to M× (more precisely, it carries a smooth structure à la Gompf) then X× 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× 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 R4’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.