Asymptotic Stability of Minkowski Space-Time with Non-compactly Supported Massless Vlasov Matter

Autor(en)

Leo Bigorgne, David Fajman, Jeremie Joudioux, Jacques Smulevici, Maximilian Thaller

Abstrakt

We prove the global asymptotic stability of the Minkowski space for the massless Einstein-Vlasov system in wave coordinates. In contrast with previous work on the subject, no compact support assumptions on the initial data of the Vlasov field in space or the momentum variables are required. In fact, the initial decay in v is optimal. The present proof is based on vector field and weighted vector field techniques for Vlasov fields, as developed in previous work of Fajman, Joudioux, and Smulevici, and heavily relies on several structural properties of the massless Vlasov equation, similar to the null and weak null conditions. To deal with the weak decay rate of the metric, we propagate well-chosen hierarchized weighted energy norms which reflect the strong decay properties satisfied by the particle density far from the light cone. A particular analytical difficulty arises at the top order, when we do not have access to improved pointwise decay estimates for certain metric components. This difficulty is resolved using a novel hierarchy in the massless Einstein-Vlasov system, which exploits the propagation of different growth rates for the energy norms of different metric components.

Organisation(en)

Gravitationsphysik

Externe Organisation(en)

University of Cambridge, Max-Planck-Institut für Gravitationsphysik (Albert Einstein Institut), Université Paris VI - Pierre-et-Marie-Curie, Chalmers University of Technology

Journal

Archive for Rational Mechanics and Analysis

Band

242

Seiten

1-147

Anzahl der Seiten

147

ISSN

0003-9527

DOI

https://doi.org/10.1007/s00205-021-01639-2

Publikationsdatum

07-2021

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

Schlagwörter

ASJC Scopus Sachgebiete

Mechanical Engineering, Analysis, Mathematics (miscellaneous)

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/4ad373ce-28ca-4646-b1e2-33cd537b127f