Stable fixed points of the Einstein flow with positive cosmological constant

Author(s)
David Fajman, Klaus Kröncke
Abstract

We prove nonlinear stability for a large class of solutions to the Einstein equations with a positive cosmological constant and compact spatial topology in arbitrary dimensions, where the spatial metric is Einstein with either positive or negative Einstein constant. The proof uses the CMC Einstein flow and stability follows by an energy argument. We prove in addition that the development of non-CMC initial data close to the background contains a CMC hypersurface, which in turn implies that stability holds for arbitrary perturbations. Furthermore, we construct a one-parameter family of initial data such that above a critical parameter value the corresponding development is future and past incomplete.

Organisation(s)
Gravitational Physics
External organisation(s)
Universität Hamburg
Journal
Communications in Analysis and Geometry
Volume
28
Pages
1533–1576
No. of pages
44
ISSN
1019-8385
DOI
https://doi.org/10.4310/CAG.2020.v28.n7.a2
Publication date
2015
Peer reviewed
Yes
Austrian Fields of Science 2012
101006 Differential geometry
Keywords
ASJC Scopus subject areas
Analysis, Geometry and Topology, Statistics and Probability, Statistics, Probability and Uncertainty
Portal url
https://ucrisportal.univie.ac.at/en/publications/438ab932-459e-4e3c-ad19-3aade43c896a