On future asymptotics of polarized Gowdy T^3-models

Gowdyʹs model of cosmological spacetimes is a much investigated subject in classical and quantum gravity. Depending on spatial topology, re-collapsing as well as expanding models are known. Several analytical tools were used in order to clarify singular behaviour in this class of spacetimes. Here we investigate the structure of a certain subclass, the polarized Gowdy models with spatial T^3-topology, in general. The asymptotics for general solutions of the dynamical equation for one of the gravitational degrees of freedom play a key role while the asymptotic behaviour of the remaining metric function is a result of solving the Hamiltonian constraint equation. Using both, we prove future geodesic completeness in all spacetimes of this type.