Abstract
In a four-dimensional Lorentzian manifold in which Einstein's gravitational field equations hold with the field produced by pressure free dust, a significant set of new solutions is found. Assuming that the manifold possesses a four parametric group of isometries of type 5 in Bianchi's classification, which act on a three-dimensional negative definite subspace, all metrics are found. The solutions are unusual in that the geodesics which the particles follow are not orthogonal to the three-dimensional negative-definite subspace so that the space will not appear homogeneous to these observers. The isotropic expansion is nonzero for almost all these solutions.
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