On almost EGS theorems

We show assuming small data that massless solutions to the reflection symmetric Einstein-Vlasov system with Bianchi VII$_0$ symmetry which are not locally rotational symmetric, can be arbitrarily close to and will remain close to isotropy as regards the shear. However in general the shear will not tend to zero and the Hubble normalised Weyl curvature will blow up. We thus have generalised the work \cite{NHW,WHU} which considered a non-tilted radiation fluid to the massless Vlasov case. This represents another example of the fact that almost-EGS theorems do not hold in general and that collisionless matter behaves differently than a perfect fluid.