Global stability of the Minkowski spacetime for the Einstein-Vlasov system

TL;DR

This paper proves the global stability of Minkowski spacetime for the Einstein-Vlasov system without compact support assumptions, allowing a broad class of perturbations and decay rates, extending previous results.

Contribution

It establishes the stability of Minkowski spacetime for the Einstein-Vlasov system without compact support or Schwarzschild exterior assumptions, broadening the class of perturbations.

Findings

Proves global stability of Minkowski spacetime for Einstein-Vlasov system.

Allows non-isotropic perturbations with decay rate ngle r^{-1+}.

Removes compact support restrictions on the Vlasov component.

Abstract

We prove global stability of the Minkowski spacetime in the wave coordinates system for the massive Einstein-Vlasov system. In particular, compared with previous results by Lindblad-Taylor, in which the Vlasov part is assumed to have compact support assumption, and Fajman-Joudioux-Smulevci, in which the spacetime is assumed to be exact Schwarzschild in the exterior region, we do not impose any compact support condition for the Vlasov part and allow a large class of non-isotropic perturbations for the metric part, which decay at rate $\langle r\rangle^{-1+}$ towards space infinity.