A class of solutions to the Einstein equations with AVTD behavior in generalized wave gauges

TL;DR

This paper proves the stability of AVTD behavior in vacuum Gowdy solutions under generalized wave gauges, extending known results beyond areal coordinates and providing a framework for analyzing more general spacetimes.

Contribution

It demonstrates the existence and stability of AVTD solutions in a broad class of gauges, generalizing previous coordinate-dependent results.

Findings

AVTD behavior is stable under gauge perturbations

Existence of smooth vacuum Gowdy solutions in generalized gauges

Framework applicable to more general spacetimes

Abstract

We establish the existence of smooth vacuum Gowdy solutions, which are asymptotically velocity term dominated (AVTD) and have T3-spatial topology, in an infinite dimensional family of generalized wave gauges. These results show that the AVTD property, which is known to hold for solutions in areal coordinates, is stable to perturbations with respect to the gauge source functions. Our proof is based on an analysis of the singular initial value problem for the Einstein vacuum equations in the generalized wave gauge formalism, and provides a framework which we anticipate to be useful for more general spacetimes.