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

TL;DR

This paper reviews methods for assessing $C^0$-extendibility of spacetimes, demonstrating that some open FLRW models, called 'Milne-like,' admit extensions through the big bang, while others are inextendible.

Contribution

It generalizes Sbierski's methodology to analyze $C^0$-extendibility of open FLRW spacetimes, introducing new results on Milne-like models.

Findings

Milne-like spacetimes admit $C^0$ extensions through the big bang.

Most non-Milne-like open FLRW models are $C^0$-inextendible within spherical symmetry.

The paper extends techniques for understanding cosmic censorship and spacetime extendibility.

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.