Nonlinear stability of self-gravitating massive fields. A wave-Klein–Gordon model

Abstract

Abstract In recent years, significant progress has been made in understanding the global evolution of self-gravitating massive matter in the small-perturbative regime near Minkowski spacetime. To investigate the interaction between a Klein–Gordon equation and Einstein’s field equations, we developed a new approach called the Euclidean-hyperboloidal foliation method. This method involves constructing a spacetime foliation that is well-suited for deriving precise decay estimates for wave and Klein–Gordon equations in curved spacetime. In this article, we provide an overview of our method and present a complete proof for a wave-Klein–Gordon model that captures some of the key challenges associated with the Einstein-matter system.