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.
Similar content being viewed by others Explore related subjectsDiscover the latest articles and news from researchers in related subjects, suggested using machine learning. Author information Authors and AffiliationsMax Planck Institut für Gravitationsphysik, Albert Einstein Institut, Am Mühlenberg 1, D-14476 Golm, Germany, e-mail: hansr@aei-potsdam.mpg.de, , , , , , DE
H. Ringström
Submitted 21/11/00, accepted 14/12/00
About this article Cite this articleRingström, H. The Bianchi IX Attractor. Ann. Henri Poincaré 2, 405–500 (2001). https://doi.org/10.1007/PL00001041
Issue Date: June 2001
DOI: https://doi.org/10.1007/PL00001041
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