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 $\Sigma^a_b\Sigma^b_a$ and $\tilde{w}^i_j \tilde{w}^j_i$ decaying as $O(t^{-\frac12})$.