Thurston's geometrization conjecture and cosmological models

We investigate a class of spatially compact inhomogeneous spacetimes. Motiv ated by Thurston's geometrization conjecture, we give a formulation for con structing spatially compact composite spacetimes as solutions for the Einst ein equations. Such composite spacetimes are built from the spatially compa ct locally homogeneous vacuum spacetimes which have two commuting local Kil ling vector fields and are homeomorphic to torus bundles over the circle by gluing them through a timelike hypersurface admitting a homogeneous spatia l torus spanned by the commuting local Killing vector fields, We also assum e that the matter which will arise from the gluing is compressed on the bou ndary, i.e, we take the thin-shell approximation. By solving the junction c onditions, we can see dynamical behaviour of the connected (composite) spac etime. The Teichmuller deformation of the torus can also be obtained. We ap ply our formalism to a concrete model. The relation to the torus sum of 3-m anifolds and the difficulty of this problem are also discussed.