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 th...
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 (1981). 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.
The SL(2) formalism of Kinnersley and Chitre (1978) for generating techniques in stationary axisymmetric vacuum space-times is adapted to work for space-times with two spacelike commuting Killing vectors. The Kinnersl...
The SL(2) formalism of Kinnersley and Chitre (1978) for generating techniques in stationary axisymmetric vacuum space-times is adapted to work for space-times with two spacelike commuting Killing vectors. The Kinnersley-Chitre formalism is known to be explicitly related to the inverse scattering transformation of Belinskii and Zakharov (1979) which has already been applied in both types of above mentioned space-times. Using the hyperbolic versions of various Kinnersley-Chitre transformations the interrelation between various vacuum cosmological solutions is obtained. For each solution the Kinnersley-Chitre generating function FAB(t) and corresponding Belinskii-Zakharov eigenfunction psi ( lambda ) is given. These vacuum solutions are then converted to scalar field/stiff perfect fluid solutions using the algorithm of Wainwright, Ince and Marshman (1979).
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