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

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.

39 pages. Typos fixed, references added and relation to previous work clarified

References in corpus (3)

• Coordinates in the relativistic Boltzmann theory
• Isotropization of non-diagonal Bianchi I spacetimes with collisionless matter at late times assuming small data
• Future non-linear stability for solutions of the Einstein-Vlasov system of Bianchi types II and VI${}_0$

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• Isotropization of Slowly Expanding Spacetimes
• Kantowski-Sachs cosmology with Vlasov matter
• The massless Einstein-Boltzmann system with a conformal-gauge singularity in an FLRW background
• Small solutions of the Einstein-Boltzmann-scalar field system with Bianchi symmetry
• Late-time behaviour of the Einstein-Boltzmann system with a positive cosmological constant
• Bianchi I solutions of the Einstein-Boltzmann system with a positive cosmological constant
• On the future of solutions to the massless Einstein-Vlasov system in a Bianchi I cosmology
• Self-similarity breaking of cosmological solutions with collisionless matter
• The spatially homogeneous Boltzmann equation for massless particles in an FLRW background
• On almost Ehlers-Geren-Sachs theorems
• Well-posedness of anisotropic and homogeneous solutions to the Einstein-Boltzmann system with a conformal-gauge singularity
• Future of Bianchi I magnetic cosmologies with kinetic matter
• Asymptotic behaviour of the Boltzmann equation as a cosmological model
• Future global existence of homogeneous solutions to the Einstein-Boltzmann system with soft potentials
• Global Dynamics for a relativistic charged and colliding plasma in presence of a massive scalar field on the Robertson-Walker spacetime