Dynamics of Bianchi Type I Solutions of the Einstein Equations with Anisotropic Matter |
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Authors: | Simone Calogero J Mark Heinzle |
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Institution: | (1) Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, E-18071 Granada, Spain;(2) Gravitational Physics, Faculty of Physics, University of Vienna, A-1090 Vienna, Austria |
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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.
Submitted: October 28, 2008.; Accepted: January 26, 2009. |
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