Starting from the proof of the \(C^0\) -inextendibility of Schwarzschild by Sbierski, the past decade has seen renewed interest in showing low-regularity inextendibility for known spacetime models. Specifically, a lot of attention has been paid to FLRW spacetimes and there is an ever-growing array of results in the literature. Apart from hoping to provide a concise summary of the state of the art, we present an extension of work by Galloway and Ling on \(C^0\) -inextendibility of certain FLRW spacetimes within a subclass of spherically symmetric spacetimes, Galloway and Ling (Ann Henri Poincaré 18(10):3427–3477, 2017), to \(C^0\) -inextendibility within a subclass of axisymmetric spacetimes. Notably, our result works in the case of flat FLRW spacetimes with \(a(t)\to 0\) for \(t\to 0^+\) , a setting where other known \(C^0\) -inextendibility results for FLRW spacetimes due to Sbierski (arXiv:2312.07443, 2023), do not apply.

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\(C^{0}\) -Inextendibility of FLRW Spacetimes Within a Subclass of Axisymmetric Spacetimes

  • Melanie Graf,
  • Marco van den Beld-Serrano

摘要

Starting from the proof of the \(C^0\) -inextendibility of Schwarzschild by Sbierski, the past decade has seen renewed interest in showing low-regularity inextendibility for known spacetime models. Specifically, a lot of attention has been paid to FLRW spacetimes and there is an ever-growing array of results in the literature. Apart from hoping to provide a concise summary of the state of the art, we present an extension of work by Galloway and Ling on \(C^0\) -inextendibility of certain FLRW spacetimes within a subclass of spherically symmetric spacetimes, Galloway and Ling (Ann Henri Poincaré 18(10):3427–3477, 2017), to \(C^0\) -inextendibility within a subclass of axisymmetric spacetimes. Notably, our result works in the case of flat FLRW spacetimes with \(a(t)\to 0\) for \(t\to 0^+\) , a setting where other known \(C^0\) -inextendibility results for FLRW spacetimes due to Sbierski (arXiv:2312.07443, 2023), do not apply.