Some Remarks on the $$C^0$$ C 0 -(In)Extendibility of Spacetimes

Autor: Eric Ling, Gregory J. Galloway
Rok vydání: 2017
Předmět:
Zdroj: Annales Henri Poincaré. 18:3427-3447
ISSN: 1424-0661
1424-0637
DOI: 10.1007/s00023-017-0602-1
Popis: 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 $$C^0$$ 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 Sbierski (The $${C}^0$$ -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 $$C^0$$ -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 admits $$C^0$$ extensions through the big bang. For spacetimes that are not Milne-like, we prove some inextendibility results within the class of spherically symmetric spacetimes.
Databáze: OpenAIRE
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