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

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 ${\mathrm{\Sigma }}_b^a{\mathrm{\Sigma }}_a^b$ and $\tilde{w}^i_j \tilde{w}^j_i$decayingas$O(t^{-\frac12})$.