Stable fixed points of the Einstein flow with positive cosmological constant

Autor(en)

David Fajman, Klaus Kröncke

Abstrakt

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(en)

Gravitationsphysik

Externe Organisation(en)

Universität Hamburg

Journal

Communications in Analysis and Geometry

Band

28

Seiten

1533–1576

Anzahl der Seiten

44

ISSN

1019-8385

DOI

https://doi.org/10.4310/CAG.2020.v28.n7.a2

Publikationsdatum

2015

Peer-reviewed

Ja

ÖFOS 2012

101006 Differentialgeometrie

Schlagwörter

ASJC Scopus Sachgebiete

Analysis, Geometry and Topology, Statistics and Probability, Statistics, Probability and Uncertainty

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/438ab932-459e-4e3c-ad19-3aade43c896a