On almost Ehlers-Geren-Sachs theorems

We show assuming small data that massless solutions to the reflection symmetric Einstein-Vlasov system with Bianchi VII₀ symmetry which are not locally rotational symmetric, can be arbitrarily close to and will remain close to isotropy as regards to the shear. However in general the shear will not tend to zero and the Hubble normalised Weyl curvature will blow up. This generalises the work (Nilsson et al 2000 Class. Quantum Grav. 17 3119-34; Wainwright et al 1999 Class. Quantum Grav. 16 2577-98), which considered a non-tilted radiation fluid to the massless Vlasov case. This represents another example of the fact that almost Ehlers-Geren-Sachs theorems do not hold in general and that collisionless matter behaves differently than a perfect fluid.