The global nonlinear stability of Minkowski spacetime for   self-gravitating massive fields. A brief overview
  This is a short review of a series of papers which, in collaboration with Yue Ma, establish several novel existence results for systems of coupled wave-Klein-Gordon equation. Our method, the Hyperbolic Hyperboloidal Method, has allowed us to address the global evolution problem for the Einstein equations of general relativity and investigate the global geometry of matter spacetimes that are initially close to Minkowski spacetime. 
Philippe G. LeFloch
math.AP gr-qc