An exact anisotropic solution of the Einstein-Liouville equations

A family of exact solutions of the Einstein-Liouville equations are presented, in which the space-time geometry is that of ak=0 ork=+1 Robertson-Walker space-time but the particle distribution function is anisotropic (and can be inhomogeneous). In some of these solutions, the fluid average (barycentric) velocity is not the timelike eigenvector of the fluid stress tensor. Then a “fundamental observer” moving with the average (barycentric) velocity will not observe these universes to be isotropic.