Flat Spacetimes with Compact Hyperbolic Cauchy Surfaces

Details Flat Spacetimes with Compact Hyperbolic Cauchy Surfaces Flat Spacetimes with Compact Hyperbolic Cauchy Surfaces

2003-11-03

arxiv.org/abs/math/0311019v1

Mathematics

Differential Geometry

59 pages, 9 figures

Scientific paper

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.

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