Nonlinear Stability of the Milne Model with Matter

Author(s)
Lars Andersson, David Fajman
Abstract

We show that any 3+1-dimensional Milne model is future nonlinearly, asymptotically stable in the set of solutions to the Einstein-Vlasov system. For the analysis of the Einstein equations we use the constant-mean-curvature-spatial-harmonic gauge. For the distribution function the proof makes use of geometric L-2-estimates based on the Sasaki-metric. The resulting estimates on the energy-momentum tensor are then upgraded by employing the natural continuity equation for the energy density. The combination of L-2-estimates and the continuity equation reveals a powerful tool to analyze massive transport equations with potential applications beyond the result presented here.

Organisation(s)
Gravitational Physics
External organisation(s)
Max-Planck-Institut für Gravitationsphysik (Albert Einstein Institut)
Journal
Communications in Mathematical Physics
Volume
378
Pages
261–298
No. of pages
38
ISSN
0010-3616
DOI
https://doi.org/10.1007/s00220-020-03745-w
Publication date
04-2020
Peer reviewed
Yes
Austrian Fields of Science 2012
103019 Mathematical physics
Keywords
ASJC Scopus subject areas
Statistical and Nonlinear Physics, Mathematical Physics
Portal url
https://ucrisportal.univie.ac.at/en/publications/0e201afd-95f8-4915-9a8e-943be245fa59