Dynamics of Bianchi type I solutions of the Einstein equations with anisotropic matter

Author(s)

Simone Calogero, Johannes Markus Heinzle

Abstract

We analyze the global dynamics of Bianchi type I solutions of the

Einstein equations with anisotropic matter. The matter model is not

specified explicitly but only through a set of mild and physically

motivated assumptions; thereby our analysis covers matter models as

different from each other as, e.g., collisionless matter, elastic matter

and magnetic fields. The main result we prove is the existence of an

‘anisotropy classification’ for the asymptotic behaviour of Bianchi type

I cosmologies. The type of asymptotic behaviour of generic solutions is

determined by one single parameter that describes certain properties of

the anisotropic matter model under extreme conditions. The anisotropy

classification comprises the following types. The convergent type A ₊:

Each solution converges to a Kasner solution as the singularity is

approached and each Kasner solution is a possible past asymptotic state.

The convergent types B ₊ and C ₊:

Each solution converges to a Kasner solution as the singularity is

approached; however, the set of Kasner solutions that are possible past

asymptotic states is restricted. The oscillatory type D ₊:

Each solution oscillates between different Kasner solutions as the

singularity is approached. Furthermore, we investigate non-generic

asymptotic behaviour and the future asymptotic behaviour of solutions.

Organisation(s)

Gravitational Physics

External organisation(s)

Universidad de Granada

Journal

Annales Henri Poincare

Volume

Pages

225-274

No. of pages

ISSN

1424-0637

DOI

https://doi.org/10.1007/s00023-009-0407-y

Publication date

2009

Peer reviewed

Yes

Austrian Fields of Science 2012

103028 Theory of relativity, 103019 Mathematical physics

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