Isotropization of non-diagonal Bianchi I spacetimes with collisionless matter at late times assuming small data

Abstract

Assuming that the space-time is close to isotropic in the sense that the shear parameter is small and that the maximal velocity of the particles is bounded, we have been able to show that for non-diagonal Bianchi I-symmetric spacetimes with collisionless matter the asymptotic behaviour at late times is close to the special case of dust. We also have been able to show that all the Kasner exponents converge to 1/3 and an asymptotic expression for the induced metric has been obtained. The key was a bootstrap argument.

V3 18 p. 3 fig. typos corrected, conclusions part extended, references added. To appear in Classical and Quantum Gravity

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Cited by in corpus (14)

• The Einstein-Vlasov System/Kinetic Theory
• Future global existence and asymptotic behaviour of solutions to the Einstein-Boltzmann system with Bianchi I symmetry
• Isotropization of Slowly Expanding Spacetimes
• Future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI${}_0$
• Stable cosmologies with collisionless charged matter
• Kantowski-Sachs cosmology with Vlasov matter
• Future attractors of Bianchi types II and V cosmologies with massless Vlasov matter
• On the future of solutions to the massless Einstein-Vlasov system in a Bianchi I cosmology
• Isotropization of solutions of the Einstein-Vlasov system with Bianchi V symmetry
• Self-similarity breaking of cosmological solutions with collisionless matter
• Late-time behaviour of the Einstein-Vlasov system with Bianchi I symmetry
• Asymptotic behaviour of the relativistic Boltzmann equation in the Robertson-Walker spacetime
• Future of Bianchi I magnetic cosmologies with kinetic matter
• States of Low Energy on Bianchi I spacetimes