Rotating Bianchi type V dust models generalizing the kÄÀ1 Friedmann model

The Einstein equations are investigated for a rotating Bianchi type V dust model in which one of the Killing fields is spanned on velocity and rotation ~case 1.2.2.2 in the classification scheme of the earlier papers!. A first integral of the field equations is found, and with a special value of this integral coordinate transformations are used to eliminate two components of the metric. The k521 Friedmann model is shown to be contained among the solutions in the limit of zero rotation. The field equations for the simplified metric are reduced to 3 second-order ordinary differential equations that determine 3 metric components plus a first integral that algebraically determines the fourth component. First derivatives of the metric components are subject to a constraint ~a second-degree polynomial with coefficients depending on the functions!. It is shown that the set does not follow from a Lagrangian of the Hilbert type. The group of Lie point-symmetries of the set is found, it is two-dimensional noncommutative. Finally, a method of searching for first integrals ~for sets of differential equations! that are polynomials of degree 1 or 2 in the first derivatives is applied. No such first integrals exist. The method is used to find a constraint ~of degree 1 in first derivatives! that could be imposed on the metric, but it leads to a vacuum solution, and so is of no interest for cosmology. © 2001 American Institute of Physics. @DOI: 10.1063/1.1330197#