Future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI${}_0$

Abstract

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.

30 pages

References in corpus (4)

• Isotropization of non-diagonal Bianchi I spacetimes with collisionless matter at late times assuming small data
• Spherical linear waves in de Sitter spacetime
• Oscillations toward the singularity of LRS Bianchi type IX cosmological models with Vlasov matter
• Dynamics of locally rotationally symmetric Bianchi type VIII cosmologies with anisotropic matter

Cited by in corpus (7)

• Future non-linear stability for solutions of the Einstein-Vlasov system of Bianchi types II and VI${}_0$
• Isotropization of Slowly Expanding Spacetimes
• Kantowski-Sachs cosmology with Vlasov matter
• Future attractors of Bianchi types II and V cosmologies with massless Vlasov matter
• Isotropization of solutions of the Einstein-Vlasov system with Bianchi V symmetry
• Self-similarity breaking of cosmological solutions with collisionless matter
• Future of Bianchi I magnetic cosmologies with kinetic matter