Some Remarks on the $C^0$-(in)extendibility of Spacetimes

Abstract

The existence, established over the past number of years and supporting earlier work of Ori [14], of physically relevant black hole spacetimes that admit $C^0$ metric extensions beyond the future Cauchy horizon, while being $C^2$-inextendible, has focused attention on fundamental issues concerning the strong cosmic censorship conjecture. These issues were recently discussed in the work of Jan Sbierski [17], in which he established the (nonobvious) fact that the Schwarschild solution in global Kruskal-Szekeres coordinates is $C^0$-inextendible. In this paper we review aspects of Sbierski's methodology in a general context, and use similar techniques, along with some new observations, to consider the $C^0$-inextendibility of open FLRW cosmological models. We find that a certain special class of open FLRW spacetimes, which we have dubbed `Milne-like,' actually admit $C^0$ extensions through the big bang. For spacetimes that are not Milne-like, we prove some inextendibility results within the class of spherically symmetric spacetimes.

22 pages, v2: minor changes and clarifications; reference added. To appear in Annales Henri Poincare

References in corpus (1)

• Pre-big bang geometric extensions of inflationary cosmologies

Cited by in corpus (22)

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• Inextendibility of spacetimes and Lorentzian length spaces
• Maximizers in Lipschitz spacetimes are either timelike or null
• The future is not always open
• On the causal hierarchy of Lorentzian length spaces
• On the proof of the $C^0$-inextendibility of the Schwarzschild spacetime
• On the initial singularity and extendibility of flat quasi-de Sitter spacetimes
• A Lorentzian analog for Hausdorff dimension and measure
• Hyperbolic angles in Lorentzian length spaces and timelike curvature bounds
• Aspects of $C^0$ causal theory
• Some regularity results for Lorentz-Finsler spaces
• The Big Bang is a Coordinate Singularity for $k=-1$ Inflationary FLRW Spacetimes
• Lorentz meets Lipschitz
• Polynomial $f(R)$ Palatini cosmology -- dynamical system approach
• Remarks on the cosmological constant appearing as an initial condition for Milne-like spacetimes
• On the asymptotic assumptions for Milne-like spacetimes
• The annoying null boundaries
• Low regularity extensions beyond Cauchy horizons
• Well-posedness of anisotropic and homogeneous solutions to the Einstein-Boltzmann system with a conformal-gauge singularity
• Uniqueness of maximal spacetime boundaries
• A lower semicontinuous time separation function for $C^0$ spacetimes
• An extendible spacetime without closed timelike curves whose every extension contains closed timelike curves