Some New General Relativistic Dust Metrics Possessing Isometries

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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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