Communications in Analysis and Geometry
Volume 28 (2020)
Stable fixed points of the Einstein flow with positive cosmological constant
Pages: 1533 – 1576
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.
Received 5 June 2015
Accepted 19 March 2018
Published 7 December 2020