Global nonlinear stability of large dispersive solutions to the Einstein equations

TL;DR

This paper proves the global nonlinear stability of a broad class of large dispersive solutions to the Einstein-scalar field system, extending previous stability results of Minkowski spacetime to more general, large data scenarios.

Contribution

It establishes the first stability results for large asymptotically flat initial data in Einstein-scalar field systems, including non-spherically symmetric perturbations.

Findings

Large dispersive solutions are future globally nonlinearly stable.

Constructs an open set of large initial data leading to complete spacetimes.

Extends stability results beyond small perturbations of Minkowski spacetime.

Abstract

We extend the monumental result of Christodoulou-Klainerman on the global nonlinear stability of the Minkowski spacetime to the global nonlinear stability of a class of large dispersive spacetimes. More precisely, we show that any regular future causally geodesically complete, asymptotically flat solution to the Einstein-scalar field system which approaches the Minkowski spacetime sufficiently fast for large times is future globally nonlinearly stable. Combining our main theorem with results of Luk-Oh, Luk-Oh-Yang and Kilgore, we prove that a class of large data spherically symmetric dispersive solutions to the Einstein-scalar field system are globally nonlinearly stable with respect to small non-spherically symmetric perturbations. This in particular gives the first construction of an open set of large asymptotically flat initial data for which the solutions to the Einstein-scalar field system are future causally geodesically complete.