A new proof of the Bianchi type IX attractor theorem

Details A new proof of the Bianchi type IX attractor theorem A new proof of the Bianchi type IX attractor theorem

2009-01-07

arxiv.org/abs/0901.0806v1

Class.Quant.Grav.26:075015,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

26 pages, 5 figures

Scientific paper

10.1088/0264-9381/26/7/075015

We consider the dynamics towards the initial singularity of Bianchi type IX vacuum and orthogonal perfect fluid models with a linear equation of state. The `Bianchi type IX attractor theorem' states that the past asymptotic behavior of generic type IX solutions is governed by Bianchi type I and II vacuum states (Mixmaster attractor). We give a comparatively short and self-contained new proof of this theorem. The proof we give is interesting in itself, but more importantly it illustrates and emphasizes that type IX is special, and to some extent misleading when one considers the broader context of generic models without symmetries.

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