Cosmic censorship near FLRW spacetimes with negative spatial curvature

Fajman, David; Urban, Liam

doi:10.2140/apde.2025.18.1615

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Cosmic censorship near FLRW spacetimes with negative spatial curvature

David Fajman and Liam Urban

Vol. 18 (2025), No. 7, 1615–1713

DOI: 10.2140/apde.2025.18.1615

Abstract

We consider general initial data for the Einstein scalar-field system on a closed $3$ -manifold $(M, γ)$ which is close to data for a Friedman–Lemaître–Robertson–Walker solution with homogeneous scalar field matter and a negative Einstein metric $γ$ as spatial geometry. We prove that the maximal globally hyperbolic development of such initial data in the Einstein scalar-field system is past incomplete in the contracting direction and exhibits stable collapse into a big bang curvature singularity. Under an additional condition on the first positive eigenvalue of $- Δ_{γ}$ satisfied, for example, by closed hyperbolic 3-manifolds of small diameter, we prove that the data evolves to a future complete spacetime in the expanding direction which asymptotes to a vacuum Friedman solution with $(M, γ)$ as the expansion normalized spatial geometry. In particular, the strong cosmic censorship conjecture holds for this class of solutions in the $C^{2}$ -sense.

Keywords

Einstein scalar-field system, stability, blow-up profile, cosmic censorship, big bang singularity

Mathematical Subject Classification

Primary: 83C75

Secondary: 35B35, 35Q76, 83C05, 83F05

Milestones

Received: 14 December 2022

Revised: 19 July 2023

Accepted: 3 June 2024

Published: 13 June 2025

Authors

David Fajman
Faculty of Physics University of Vienna Vienna Austria

Liam Urban
Faculty of Mathematics University of Vienna Vienna Austria

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Vol. 18, No. 7, 2025