An Invitation to Lorentzian Geometry
arXiv:math/0604265
Abstract
The intention of this article is to give a flavour of some global problems in General Relativity. We cover a variety of topics, some of them related to the fundamental concept of 'Cauchy hypersurfaces': (1) structure of globally hyperbolic spacetimes, (2) the relativistic initial value problem, (3) constant mean curvature surfaces, (4) singularity theorems, (5) cosmic censorship and Penrose inequality, (6) spinors and holonomy.
This new version extends and updates widely the previous one, with new topics and around the the double of pages and references. 34 pages, Latex
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