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Communications in Mathematical Physics

, Volume 350, Issue 2, pp 803–844 | Cite as

Sharp Asymptotics for Einstein-\({\lambda}\)-Dust Flows

  • Helmut FriedrichEmail author
Open Access
Article

Abstract

We consider the Einstein-dust equations with positive cosmological constant \({\lambda}\) on manifolds with time slices diffeomorphic to an orientable, compact 3-manifold \({S}\). It is shown that the set of standard Cauchy data for the Einstein-\({\lambda}\)-dust equations on \({S}\) contains an open (in terms of suitable Sobolev norms) subset of data which develop into solutions that admit at future time-like infinity a space-like conformal boundary \({{\mathcal J}^+}\) that is \({C^{\infty}}\) if the data are of class \({C^{\infty}}\) and of correspondingly lower smoothness otherwise. The class of solutions considered here comprises non-linear perturbations of FLRW solutions as very special cases. It can conveniently be characterized in terms of asymptotic end data induced on \({{\mathcal J}^+}\). These data must only satisfy a linear differential equation. If the energy density is everywhere positive they can be constructed without solving differential equations at all.

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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Max-Planck-Institut für GravitationsphysikGolmGermany

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