The global nonlinear stability of Minkowski space for the massless Einstein--Vlasov system

TL;DR

This paper proves the global nonlinear stability of Minkowski space when coupled with the massless Einstein--Vlasov system, demonstrating that small perturbations do not lead to singularities and the spacetime remains close to flat.

Contribution

It establishes the first global stability result for Minkowski space in the massless Einstein--Vlasov setting, extending previous vacuum stability results to include massless matter fields.

Findings

Minkowski space remains stable under massless Einstein--Vlasov evolution.

Matter remains supported in the wave zone during evolution.

Weighted estimates and geometric analysis are key to the proof.

Abstract

Minkowski space is shown to be globally stable as a solution to the Einstein--Vlasov system in the case when all particles have zero mass. The proof proceeds by showing that the matter must be supported in the "wave zone", and then proving a small data semi-global existence result for the characteristic initial value problem for the massless Einstein--Vlasov system in this region. This relies on weighted estimates for the solution which, for the Vlasov part, are obtained by introducing the Sasaki metric on the mass shell and estimating Jacobi fields with respect to this metric by geometric quantities on the spacetime. The stability of Minkowski space result for the vacuum Einstein equations is then appealed to for the remaining regions.