English

Future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a cosmological constant

Mathematical Physics 2024-06-18 v1 General Relativity and Quantum Cosmology math.MP

Abstract

We show future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a positive cosmological constant. Estimates of higher derivatives of the metric and the matter terms are obtained using an inductive argument. In a recent research monograph Ringstr\"{o}m shows future non-linear stability of (not necessarily symmetric) solutions of the Einstein-Vlasov system with a non-linear scalar field if certain local estimates on the geometry and the matter terms are fulfilled. We show that these assumptions are satisfied at late times for the case under consideration here which together with Cauchy stability leads to our main conclusion.

Keywords

Cite

@article{arxiv.1402.7085,
  title  = {Future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a cosmological constant},
  author = {Ernesto Nungesser},
  journal= {arXiv preprint arXiv:1402.7085},
  year   = {2024}
}

Comments

18 pages, submitted to JHDE. arXiv admin note: text overlap with arXiv:1306.6223 by other authors