Curvature blow up in Bianchi VIII and IX vacuum spacetimes

TL;DR

This paper proves that certain Bianchi VIII and IX vacuum spacetimes develop unbounded curvature, making their maximal developments inextendible and indicating singularities in these models.

Contribution

It establishes the inextendibility and curvature blow-up for non-Taub-NUT Bianchi IX and non-NUT Bianchi VIII vacuum spacetimes, advancing understanding of their singularity structure.

Findings

Maximal developments are C2 inextendible.

Curvature invariant is unbounded along incomplete geodesics.

Results apply to non-Taub-NUT Bianchi IX and non-NUT Bianchi VIII models.

Abstract

The maximal globally hyperbolic development of non-Taub-NUT Bianchi IX vacuum initial data and of non-NUT Bianchi VIII vacuum initial data is C2 inextendible. Furthermore, a curvature invariant is unbounded in the incomplete directions of inextendible causal geodesics.