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

TL;DR

This paper proves the first rigorous mathematical result demonstrating the global nonlinear stability of Minkowski space when coupled with self-gravitating massive fields, confirming the stability of such systems under small initial perturbations.

Contribution

It extends the Hyperboloidal Foliation Method to establish global existence for Einstein equations coupled with massive fields, solving a major open problem in General Relativity.

Findings

Excludes the existence of unstable self-gravitating massive fields.

Establishes global-in-time existence for coupled Einstein-Klein-Gordon system.

Provides a new framework for analyzing stability in General Relativity.

Abstract

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.