The Bianchi IX attractor

Details The Bianchi IX attractor The Bianchi IX attractor

2000-06-10

arxiv.org/abs/gr-qc/0006035v1

Annales Henri Poincare 2 (2001) 405-500

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

82 pages and 8 figures

Scientific paper

We consider the asymptotic behaviour of spatially homogeneous spacetimes of Bianchi type IX close to the singularity (we also consider some of the other Bianchi types, e. g. Bianchi VIII in the stiff fluid case). The matter content is assumed to be an orthogonal perfect fluid with linear equation of state and zero cosmological constant. In terms of the variables of Wainwright and Hsu, we have the following results. In the stiff fluid case, the solution converges to a point for all the Bianchi class A types. For the other matter models we consider, the Bianchi IX solutions generically converge to an attractor consisting of the closure of the vacuum type II orbits. Furthermore, we observe that for all the Bianchi class A spacetimes, except those of vacuum Taub type, a curvature invariant is unbounded in the incomplete directions of inextendible causal geodesics.

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