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

Ellery Ames (1) , Florian Beyer (2) , James Isenberg (3) , Philippe G. LeFloch (2)

1 Chalmers University of Technology [Göteborg]
2 LJLL - Laboratoire Jacques-Louis Lions
3 University of Oregon [Eugene]

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 has so far been known to hold for solutions in areal coordinates only, is stable to perturbations of the coordinate systems. 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.

Domaines: Equations aux dérivées partielles [math.AP]

Ellery Ames, Florian Beyer, James Isenberg, Philippe G. LeFloch. A class of solutions to the Einstein equations with AVTD behavior in generalized wave gauges. 2016. ⟨hal-01271813v3⟩