2003/11/03 by Francesco Bonsante, Bonsante, Francesco · 2 citations
Mathematics · Physics and Astronomy · #53C50 (primary) 83C99 57M50 (secondary) #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Relativity and Gravitational Theory #math-ph #math.DG #math.MP #msc:53C50 #msc:57M50 #msc:83C99
paper · pdf · doi:10.48550/arxiv.math/0311019
59 pages, 9 figures
arxiv created 2003/11/03 · openalex publication_date 2003/11/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the flat (n+1)-spacetimes admitting a Cauchy surface diffeomorphic to a compact hyperbolic n-manifold. We show how to construct a canonical future complete one among all such spacetimes sharing the same holonomy. We study the geometry of such a spacetime in terms of its canonical cosmological time. In particular we study the asymptotic behaviour of the level surfaces of the cosmological time. The present work generalizes the case n=2 treated by Mess, taking from a work of Benedetti and Guadagnini the emphasis on the fundamental role played by the canonical cosmological time.