On the Vilenkin boundary condition proposal in anisotropic universes

We show that the Vilenkin boundary condition proposal, as formulated in terms of the Klein-Gordon type current, does not specify a unique wave function in the vacuum minisuperspace models of the Kantowski-Sachs type and the locally rotationally symmetric Bianchi type III. The underlying reasons are directly in the classical dynamics of the models. We also discuss the suggestion of relating the Vilenkin proposal to a lorentzian path integral with the causal boundary condition advocated by Teitelboim. (orig.)