Global nonlinear stability of Minkowski space for spacelike-characteristic initial data

TL;DR

This paper proves the global nonlinear stability of Minkowski space for Einstein vacuum equations with spacelike-characteristic initial data, extending previous results to a new geometric setting using advanced methods.

Contribution

It introduces new geometric constructions and techniques for analyzing stability in the spacelike-characteristic setting, expanding the scope of prior stability results.

Findings

Proves global nonlinear stability of Minkowski space with spacelike-characteristic data

Develops new geometric tools for Einstein vacuum equations

Extends stability results beyond spacelike initial data

Abstract

In this paper, we prove the global nonlinear stability of Minkowski space in the context of the spacelike-characteristic Cauchy problem for Einstein vacuum equations. Spacelike-characteristic initial data are posed on a compact 3-disk and on the future complete null hypersurface emanating from its boundary. Our result extends the seminal stability result for Minkowski space proved by Christodoulou and Klainerman for which initial data are prescribed on a spacelike 3-plane. The proof relies on the classical vectorfield method and bootstrapping argument from Christodoulou-Klainerman. The main novelty is the introduction and control of new geometric constructions adapted to the spacelike-characteristic setting. In particular, it features null cones with prescribed vertices, spacelike maximal hypersurfaces with prescribed boundaries and global harmonic coordinates on Riemannian 3-disks.