On tilted perfect fluid Bianchi type VI${}_0$ self-similar models

We show that the tilted perfect fluid Bianchi VI${}_0$ family of self-similar models found by Rosquist and Jantzen [K. Rosquist and R. T. Jantzen, \emph{% Exact power law solutions of the Einstein equations}, 1985 Phys. Lett. $\mathbf{\text{107}}$A 29-32] is the most general class of tilted self-similar models but the state parameter $\gamma$ lies in the interval $(\frac{6}{5},\frac{3}{2})$. The model has a four dimensional stable manifold indicating the possibility that it may be future attractor, at least for the subclass of tilted Bianchi VI${}_0$ models satisfying $n_{\alpha }^{\alpha }=0$ in which it belongs. In addition the angle of tilt is asymptotically significant at late times suggesting that for the above subclasses of models the tilt is asymptotically extreme.