The future asymptotics of Bianchi VIII vacuum solutions

TL;DR

This paper investigates the long-term future behavior of Bianchi VIII vacuum solutions to Einstein's equations, providing both analytical and geometric insights into their asymptotic properties.

Contribution

It offers a detailed analysis of the asymptotic behavior of Bianchi VIII vacuum solutions using a specific formulation and interprets these results geometrically.

Findings

Solutions are causally geodesically complete to the future.

The asymptotic behavior of solutions is characterized in the chosen variables.

A geometric interpretation of the asymptotics is provided through the evolution of the Riemannian metric.

Abstract

Bianchi VIII vacuum solutions to Einstein's equations are causally geodesically complete to the future, given an appropriate time orientation, and the objective of this article is to analyze the asymptotic behaviour of solutions in this time direction. For the Bianchi class A spacetimes, there is a formulation of the field equations that was presented in an article by Wainwright and Hsu, and we analyze the asymptotic behaviour of solutions in these variables. We also try to give the analytic results a geometric interpretation by analyzing how a normalized version of the Riemannian metric on the spatial hypersurfaces of homogeneity evolves.