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

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 solution...

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Bibliographic Details
Published in:Journal of geometry and physics 2017-11, Vol.121, p.42-71
Main Authors: Ames, Ellery, Beyer, Florian, Isenberg, James, LeFloch, Philippe G.
Format: Article
Language:English
Subjects:
Einstein equation
Fuchsian analysis
Gowdy spacetime
Wave gauge
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Summary: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.
ISSN:0393-0440
1879-1662
1879-1662
DOI:10.1016/j.geomphys.2017.06.005