Some Remarks on the C⁰ -(In)Extendibility of Spacetimes

The existence, established over the past number of years and supporting earlier work of Ori (Phys Rev Lett 68(14):2117–2120, 1992), of physically relevant black hole spacetimes that admit C⁰ metric extensions beyond the future Cauchy horizon, while being C²-inextendible, has focused attention on fundamental issues concerning the strong cosmic censorship conjecture. These issues were recently discussed in the work of Sbierski (The C⁰-inextendibility of the Schwarzschild spacetime and the spacelike diameter in Lorentzian geometry. arXiv:1507.00601v2, (to appear in J. Diff. Geom.), 2015), in which he established the (nonobvious) fact that the Schwarzschild solution in global Kruskal–Szekeres coordinates is C⁰-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 C⁰-inextendibility of open FLRW cosmological models. We find that a certain special class of open FLRW spacetimes, which we have dubbed ‘Milne-like,’ actually admits C⁰ extensions through the big bang. For spacetimes that are not Milne-like, we prove some inextendibility results within the class of spherically symmetric spacetimes.