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://ucris.univie.ac.at/portal/en/publications/stable-fixed-points-of-the-einstein-flow-with-positive-cosmological-constant(438ab932-459e-4e3c-ad19-3aade43c896a).html