Cosmological time versus CMC time I: Flat spacetimes

Details Cosmological time versus CMC time I: Flat spacetimes Cosmological time versus CMC time I: Flat spacetimes

2006-04-22

arxiv.org/abs/math/0604486v2

Mathematics

Differential Geometry

22 pages, improved presentation

Scientific paper

This paper gives a new proof that maximal, globally hyperbolic, flat spacetimes of dimension $n\geq 3$ with compact Cauchy hypersurfaces are globally foliated by Cauchy hypersurfaces of constant mean curvature, and that such spacetimes admit a globally defined constant mean curvature time function precisely when they are causally incomplete. The proof, which is based on using the level sets of the cosmological time function as barriers, is conceptually simple and will provide the basis for future work on constant mean curvature time functions in general constant curvature spacetimes, as well for an analysis of the asymptotics of constant mean foliations.

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