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arXiv · 1506.02440

Future global existence and asymptotic behaviour of solutions to the Einstein-Boltzmann system with Bianchi I symmetry

Ho Lee·Ernesto Nungesser
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Abstract

In this paper we study the Einstein-Boltzmann system with Bianchi I symmetry. Isotropization of Bianchi I spacetimes was proved in [13] in the Vlasov case, and asymptotic behaviour of the relativistic Boltzmann equation was studied in [9] in the isotropic case. These results are generalized in the present paper to the non-isotropic and Boltzmann case. We assume that the initial data are small in a suitable sense, and show that solutions of the Einstein-Boltzmann system are future geodesically complete, that they isotropize and have a dust-like behaviour at late times. Detailed information about the metric and the matter terms is obtained. In short, the solution is asymptotically the Einstein-de Sitter solution.

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Ho Lee, Ernesto Nungesser. 2015-06-08. Future global existence and asymptotic behaviour of solutions to the Einstein-Boltzmann system with Bianchi I symmetry. https://doi.org/10.1016/j.jde.2017.02.004

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