2006/04/22 by Lars Andersson, Thierry Barbot, Andersson, Lars +5
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.math/0604486
openalex publication_date 2006/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This paper gives a new proof that maximal, globally hyperbolic, flat spacetimes of dimension n≥ 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.