The application of the homogeneous Hilbert problem of Hauser and Ernst to cosmological models with spatial axes of symmetry

Open and closed vacuum and scalar field/stiff perfect fluid cosmological models requiring more than one canonical coordinate patch to cover the entire spacetime are treated. The boundary conditions which are met on the spatial axes of symmetry and the matching conditions which hold on the null hypersurfaces joining separate canonical coordinate patches are given. It is shown how all such cosmological solutions may be generated from flat space using the homogeneous Hilbert problem of Hauser and Ernst. Specific solutions considered include the Gowdy solutions, the Friedmann-Robertson-Walker (FRW) models, the Kantowski-Sachs universe, locally rotationally symmetric Bianchi type I, II, III, VIII, IX models and Belinskii's solitonic perturbations of the FRW models.