CMC foliations of open spacetimes asymptotic to open Robertson-Walker spacetimes

DOI10.4310/PAMQ.2021.V17.N1.A8zbMATH Open1466.35160arXiv1902.02853OpenAlexW3162333447MaRDI QIDQ2025311

Claus Gerhardt

Publication date: 12 May 2021

Published in: Pure and Applied Mathematics Quarterly (Search for Journal in Brave)

Abstract: We consider open globally hyperbolic spacetimes $N$ of dimension $n+1$, $nge3$, which are spatially asymptotic to a Robertson-Walker spacetime or an open Friedmann universe with spatial curvature $ildekappa=0,-1$ and prove, under reasonable assumptions, that there exists a unique foliation by hypersurfaces of constant mean curvature and that the mean curvature function $au$ is a smooth time function if $N$ is smooth. Moreover, among the Friedmann universes which satisfy the necessary conditions are those that reflect the present assumptions of the development of the universe.

Full work available at URL: https://arxiv.org/abs/1902.02853

zbMATH Keywords

inverse mean curvature flowLorentzian manifoldgeneral relativitymasscosmological spacetimeARW spacetimes

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Elliptic equations on manifolds, general theory (58J05) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Flows related to mean curvature (53E10)

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