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Future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI0

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons20695

Nungesser,  Ernesto
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1208.4231
(Preprint), 329KB

Nungesser.pdf
(beliebiger Volltext), 381KB

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Zitation

Nungesser, E. (2013). Future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI0. Annales Henri Poincare, 14, 967-999. doi:10.1007/s00023-012-0201-0.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0010-0D2A-E
Zusammenfassung
Using the methods developed for the Bianchi I case we have shown that a boostrap argument is also suitable to treat the future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI$_0$. These solutions are asymptotic to the Collins-Stewart solution with dust and the Ellis-MacCallum solution respectively. We have thus generalized the results obtained by Rendall and Uggla in the case of locally rotationally symmetric Bianchi II spacetimes to the reflection symmetric case. However we needed to assume small data. For Bianchi VI$_0$ there is no analogous previous result.