Cosmic Censorship near FLRW spacetimes with negative spatial curvature

Author(s)
David Fajman, Liam Dylan Urban
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 −Δγ 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 C2-sense.

Organisation(s)
Gravitational Physics, Department of Mathematics
Journal
Analysis & PDE
Volume
7
Pages
1615-1713
ISSN
2157-5045
DOI
https://doi.org/10.2140/apde.2025.18.1615
Publication date
06-2025
Peer reviewed
Yes
Austrian Fields of Science 2012
101002 Analysis, 103028 Theory of relativity
Keywords
Portal url
https://ucrisportal.univie.ac.at/en/publications/dbab323c-3792-4630-969a-f44d735b51d0