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The future asymptotics of Bianchi VIII vacuum solutions

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 paper is to analyse 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 will analyse the asymptotic behaviour of solutions in these variables. We also try to give the analytic results a geometric interpretation by analysing how a normalized version of the Riemannian metric on the spatial hypersurfaces of homogeneity evolves.