The Einstein-Klein-Gordon coupled system: global stability of the Minkowski solution

TL;DR

This paper establishes the global stability of Minkowski space within the Einstein-Klein-Gordon system, demonstrating long-term regularity, precise asymptotics, and energy estimates for small perturbations.

Contribution

It provides the first comprehensive proof of global regularity and detailed asymptotic behavior for solutions of the Einstein-Klein-Gordon system near Minkowski space.

Findings

Global regularity of solutions under small perturbations

Asymptotic profiles and convergence rates of the metric and field

Bounds on curvature, energy, and geodesic behavior at infinity

Abstract

We prove definitive results on the global stability of the flat space among solutions of the Einstein-Klein-Gordon system. Our main theorems in this monograph include: (1) A proof of global regularity (in wave coordinates) of solutions of the Einstein-Klein-Gordon coupled system, in the case of small, smooth, and localized perturbations of the stationary Minkowski solution; (2) Precise asymptotics of the metric components and the Klein-Gordon field as the time goes to infinity, including the construction of modified (nonlinear) scattering profiles and quantitative bounds for convergence; (3) Classical estimates on the solutions at null and timelike infinity, such as bounds on the metric components, weak peeling estimates of the Riemann curvature tensor, ADM and Bondi energy identities and estimates, and asymptotic description of null and timelike geodesics.