Smooth globally hyperbolic splittings and temporal functions

Details Smooth globally hyperbolic splittings and temporal functions Smooth globally hyperbolic splittings and temporal functions

2004-04-20

arxiv.org/abs/gr-qc/0404084v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, Contribution to Proc. II Int. Meeting on Lorentzian Geometry, Murcia (Spain), November 12-14, 2003

Scientific paper

Geroch's theorem about the splitting of globally hyperbolic spacetimes is a central result in global Lorentzian Geometry. Nevertheless, this result was obtained at a topological level, and the possibility to obtain a metric (or, at least, smooth) version has been controversial since its publication in 1970. In fact, this problem has remained open until a definitive proof, recently provided by the authors. Our purpose is to summarize the history of the problem, explain the smooth and metric splitting results (including smoothability of time functions in stably causal spacetimes), and sketch the ideas of the solution.

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