Description
I will present a work in collaboration with P.G. LeFloch and Yue Ma on the nonlinear stability of Minkowski spacetime. We consider the massive Einstein-Dirac system and investigate the global evolution problem when the initial data are sufficiently close to those describing a spacelike, asymptotically Euclidean slice in Minkowski spacetime. We establish the existence of a globally hyperbolic development that remains asymptotic to Minkowski spacetime in the future timelike, null, and spacelike directions. Previous results on this problem have been limited to the massless Einstein-Dirac system. Our analysis follows closely the asymptotically hyperboloidal-Euclidean framework introduced by LeFloch and Yue Ma for the massive Klein-Gordon-Einstein system. The structure specific to spinor fields and the Dirac equation necessitates significantly new elements in the proof. In contrast with prior approaches, our treatment of spinor fields and the Dirac equation is fully gauge-invariant, relying on the formalism of Lorentz Clifford algebras, principal fiber bundles, and Dirac forms.