The future asymptotics of Bianchi VIII vacuum solutions

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.

34 pages, no figures

References in corpus (1)

• Bianchi VIII Empty Futures

Cited by in corpus (14)

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• Applications of the theory of evolution equations to general relativity
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• Dynamics of locally rotationally symmetric Bianchi type VIII cosmologies with anisotropic matter
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• The late-time behaviour of tilted Bianchi type VIII universes in presence of diffusion
• Cosmological models and stability
• Future geodesic completeness of some spatially homogeneous solutions of the vacuum Einstein equations in higher dimensions
• Report on GRG18, Session A3, Mathematical Studies of the Field Equations