$C^0$-inextendibility of the Kasner spacetime

TL;DR

This paper proves that the Kasner spacetime cannot be extended as a Lorentzian manifold even with a continuous metric, strengthening previous results on its inextendibility.

Contribution

It extends the known $C^0$-inextendibility results from Schwarzschild spacetime to the Kasner spacetime, a different cosmological model.

Findings

Kasner spacetime is $C^0$-inextendible.

The proof adapts methods from Schwarzschild spacetime inextendibility.

The result applies to the maximal analytically extended Kasner spacetime.

Abstract

The Kasner spacetime is a cosmological model of an anisotropic expanding universe without matter and is an exact solution of the Einstein vacuum equations Ric(g) = 0. It is manifestly inextendible as a Lorentzian manifold with a twice differentiable metric. In this thesis we proof that it is even inextendible as a Lorentzian manifold with merely continuous metric, which is a stronger statement. We do so by adapting the proof of the $C^0$-inextendibility of the maximal analytically extended Schwarzschild spacetime established by Jan Sbierski.