On the future of solutions to the massless Einstein-Vlasov system in a Bianchi I cosmology

Abstract

We show that massless solutions to the Einstein-Vlasov system in a Bianchi I space-time with small anisotropy, i.e. small shear and small trace-free part of the spatial energy momentum tensor, tend to a radiation fluid in an Einstein-de Sitter space-time with the anisotropy ${\Sigma }_b^a{\Sigma }_a^b$ and ${\tilde{w}}_j^i{\tilde{w}}_i^j$ decaying as $O(t^{-\frac{1}{2}})$.

11 pages. In this version V2 errata corrected (in particular decay rates of anisotropy) and references added

References in corpus (4)

• Isotropization of non-diagonal Bianchi I spacetimes with collisionless matter at late times assuming small data
• Isotropic cosmological singularities in spatially-homogeneous models with a cosmological constant
• Isotropization of Slowly Expanding Spacetimes
• Kantowski-Sachs cosmology with Vlasov matter

Cited by in corpus (3)

• Future attractors of Bianchi types II and V cosmologies with massless Vlasov matter
• On almost Ehlers-Geren-Sachs theorems
• Future of Bianchi I magnetic cosmologies with kinetic matter