Aperiodic oscillatory asymptotic behavior for some Bianchi spacetimes

Details Aperiodic oscillatory asymptotic behavior for some Bianchi spacetimes Aperiodic oscillatory asymptotic behavior for some Bianchi spacetimes

2010-04-17

arxiv.org/abs/1004.2984v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages, 1 figure

Scientific paper

We study the asymptotic behavior of type A vacuum Bianchi spacetimes. It has been conjectured that this behavior is driven by a certain circle map, called the Kasner map. As a step towards this conjecture, we prove that some orbits of the Kasner map do indeed attract some solutions of the system of ODEs which describes the behavior of type A vacuum Bianchi spacetimes. The orbits of the Kasner map for which we can prove such a result are those which are not periodic and which do not accumulate on any periodic orbit. This shows the existence of Bianchi spacetimes with a aperiodic oscillatory asymptotic behavior.

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