Some Remarks on the $C^0$-(in)extendibility of Spacetimes. (arXiv:1610.03008v2 [math.DG] UPDATED)

The discovery over the past number of years 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 work of Jan Sbierski [16], 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. 查看全文>>