$C^{0}$-inextendibility of FLRW spacetimes within a subclass of axisymmetric spacetimes

TL;DR

This paper extends the proof of $C^0$-inextendibility from spherically symmetric to axisymmetric FLRW spacetimes, including flat models with vanishing scale factor at initial time, broadening the class of known inextendible cosmological solutions.

Contribution

It generalizes existing $C^0$-inextendibility results to a wider class of axisymmetric FLRW spacetimes, especially those with zero scale factor at initial singularity.

Findings

Proves $C^0$-inextendibility for certain axisymmetric FLRW spacetimes.

Includes flat FLRW models with $a(t) o 0$ as $t o 0^+$.

Extends previous results beyond spherically symmetric cases.

Abstract

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, 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 do not apply.