Future global existence and asymptotic behaviour of solutions to the Einstein-Boltzmann system with Bianchi I symmetry
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2015
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| _version_ | 1866913392652976128 |
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| author | Lee, Ho Nungesser, Ernesto |
| author_facet | Lee, Ho Nungesser, Ernesto |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1506_02440 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Future global existence and asymptotic behaviour of solutions to the Einstein-Boltzmann system with Bianchi I symmetry Lee, Ho Nungesser, Ernesto General Relativity and Quantum Cosmology 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. |
| title | Future global existence and asymptotic behaviour of solutions to the Einstein-Boltzmann system with Bianchi I symmetry |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/1506.02440 |