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

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Abstract

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.

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Acknowledgements

The authors would like to express their thanks to Piotr Chruściel for his interest in this work and for many valuable comments. The work of GJG was partially supported by NSF Grant DMS-1313724.

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  1. Department of Mathematics, University of Miami, Coral Gables, FL , 33124, USA

    Gregory J. Galloway & Eric Ling

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  1. Gregory J. Galloway
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  2. Eric Ling
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Correspondence to Gregory J. Galloway.

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Communicated by James A. Isenberg.

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Galloway, G.J., Ling, E. Some Remarks on the \(C^0\)-(In)Extendibility of Spacetimes. Ann. Henri Poincaré 18, 3427–3447 (2017). https://doi.org/10.1007/s00023-017-0602-1

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  • DOI: https://doi.org/10.1007/s00023-017-0602-1

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