Asymptotic Behavior of a Class of Expanding Gowdy Spacetimes

TL;DR

This paper develops an asymptotic expansion for gravitational waves in expanding vacuum Gowdy spacetimes, showing that these models tend toward spatial homogeneity and identifying the asymptotic cosmological behavior.

Contribution

It introduces a systematic method to analyze the asymptotic behavior of gravitational waves in Gowdy spacetimes and links the evolution to a target space orbit decay.

Findings

Orbit circumference in target space decays to zero

Spacetime becomes spatially homogeneous asymptotically

Metric function determined by gravitational wave energy

Abstract

A systematic asymptotic expansion is developed for the gravitational wave degrees of freedom of a class of expanding, vacuum Gowdy cosmological spacetimes. In the wave map description of these models, the evolution of the gravitational wave amplitudes defines an orbit in the target space. The circumference of this orbit decays to zero indicating that the asymptotic spacetime is spatially homogeneous. A prescription is given to identify the asymptotic cosmological model for the gravitational wave degrees of freedom using the asymptotic point in the target space. The remaining metric function of the asymptotic cosmological model, found by solving the constraints, is determined by an effective energy of the gravitational waves rather than from the asymptotic point in the target space.