A new proof of the Bianchi type IX attractor theorem

Author(s)
Johannes Markus Heinzle, Claes Uggla
Abstract

We consider the dynamics toward 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.

Organisation(s)
Gravitational Physics
External organisation(s)
Karlstad University
Journal
Classical and Quantum Gravity
Volume
26
No. of pages
34
ISSN
0264-9381
DOI
https://doi.org/10.1088/0264-9381/26/7/075015
Publication date
2009
Peer reviewed
Yes
Austrian Fields of Science 2012
103028 Theory of relativity, 103019 Mathematical physics
Portal url
https://ucris.univie.ac.at/portal/en/publications/a-new-proof-of-the-bianchi-type-ix-attractor-theorem(9fffd6ab-17d4-4bce-8c80-fe1d494c14e5).html