Global Existence for the Einstein Vacuum Equations in Wave Coordinates
Abstract
We prove global stability of Minkowski space for the Einstein vacuum equations in harmonic (wave) coordinate gauge for the set of restricted data coinciding with the Schwarzschild solution in the neighborhood of spacelike infinity. The result contradicts previous beliefs that wave coordinates are "unstable in the large" and provides an alternative approach to the stability problem originally solved ( for unrestricted data, in a different gauge and with a precise description of the asymptotic behavior at null infinity) by D. Christodoulou and S. Klainerman.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 May 2005
 DOI:
 10.1007/s0022000412816
 arXiv:
 arXiv:math/0312479
 Bibcode:
 2005CMaPh.256...43L
 Keywords:

 Mathematics  Analysis of PDEs;
 General Relativity and Quantum Cosmology;
 Mathematical Physics
 EPrint:
 64 pages, no figures, submitted, CMP Minor changes and corrections added