On future asymptotics of polarized Gowdy T^3-models

TL;DR

This paper analyzes the asymptotic behavior of polarized Gowdy T^3 cosmological models, proving future geodesic completeness for all solutions by studying their asymptotics and solving the Hamiltonian constraint.

Contribution

It provides a detailed analysis of the asymptotic structure of polarized Gowdy T^3 models and establishes future geodesic completeness for this class of spacetimes.

Findings

Proved future geodesic completeness of polarized Gowdy T^3 models.

Analyzed asymptotic behavior of gravitational degrees of freedom.

Solved the Hamiltonian constraint to determine metric function asymptotics.

Abstract

Gowdy's model of cosmological spacetimes is a much investigated subject in classical and quantum gravity. Depending on spatial topology recollapsing as well as expanding models are known. Several analytic 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 the large. The asymptotics for general solutions of the dynamical equation for one of the gravitational degrees of freedom plays a key role while the asymptotic behaviour of the remaining metric function is a result of solving the Hamiltonian constraint equation. Using both we are able to prove (future) geodesic completeness in all spacetimes of this type.