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Future Non-Linear Stability for Reflection Symmetric Solutions of the Einstein-Vlasov System of Bianchi Types II and VI_0

机译:Bianchi II型和VI_0型Einstein-Vlasov系统的反射对称解的未来非线性稳定性

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摘要

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.
机译:使用针对Bianchi I案例开发的方法,我们证明了boostrap参数也适用于处理Bianchi II型和VI_0型Einstein-Vlasov系统的反射对称解的未来非线性稳定性。这些解决方案分别对应于带尘埃的Collins-Stewart解决方案和Ellis-MacCallum解决方案。因此,我们将Rendall和Uggla在局部旋转对称的Bianchi II时空情况下推广到了反射对称情况下。但是,我们需要假设少量数据。对于Bianchi VI_0,没有类似的先前结果。

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