The global nonlinear stability of Minkowski space for self-gravitating massive fields

Philippe G Lefloch (1) , Yue Ma (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 Xjtu - Xi'an Jiaotong University

The theory presented in this monograph establishes the first mathematically rigorous result on the global nonlinear stability of self-gravitating matter under small perturbations of an asymptotically flat, spacelike hypersurface of Minkowski spacetime. It allows one to exclude the existence of dynamically unstable, self-gravitating massive fields and, therefore, solves a long-standing open problem in General Relativity. By a significant extension of the Hyperboloidal Foliation Method they introduced in 2014, the authors establish global-in-time existence for the Einstein equations expressed as a coupled wave-Klein-Gordon system of partial differential equations. The metric and matter fields are sought for in Sobolev-type functional spaces, suitably defined from the translations and the boosts of Minkowski spacetime.

Mots clés: Einstein equations; massive field; global Cauchy development; Minkowski space; quasi-null nonlinearity; coupled wave-Klein-Gordon system; hyperboloidal foliation method.

Domaines: Equations aux dérivées partielles [math.AP]

Philippe G Lefloch, Yue Ma. The global nonlinear stability of Minkowski space for self-gravitating massive fields. 2015. ⟨hal-01423475v2⟩