The Bianchi IX Attractor
By Hans Ringstrom. 2000
169 citations recorded by the source corpus.
Abstract. 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.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/519247e54f2c867c5e19d278da7a0e138aa6ff13
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Citations in the corpus
- Future stability of the Einstein-non-linear scalar field system (2008, background): “1 of [30], one can apply an orthogonal matrix to the basis ei, so that ν ij with respect to this new basis is diagonal.”
- Cosmological Billiards (2002, result): “By contrast, rigorous results are rare for the case of infinitely many collisions (see, however, the recent analytic advances in [91]).”