Cauchy Hypersurfaces and Global Lorentzian Geometry

Details Cauchy Hypersurfaces and Global Lorentzian Geometry Cauchy Hypersurfaces and Global Lorentzian Geometry

2006-04-12

arxiv.org/abs/math/0604265v1

Mathematics

Differential Geometry

19 pages, no figures. Proc. XIV Fall Workshop Geom. Phys., Bilbao (Spain) September 14-16 (2005), Publ. RSME

Scientific paper

Our purpose is to give a taste on some global problems in General Relativity, to an audience with a basic knowledge on intrinsic Differential Geometry. We focus on the following problems related to the fundamental concept of {\em Cauchy hypersurface}: (1) smoothability and structure of globally hyperbolic spacetimes, (2) initial value problem, (3) singularity theorems, (4) cosmic censorship and Penrose inequality. Finally, some open questions are commented.

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