Recent progress on the notion of global hyperbolicity

Details Recent progress on the notion of global hyperbolicity Recent progress on the notion of global hyperbolicity

2007-12-12

arxiv.org/abs/0712.1933v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, 1 figure. Extended and updated contribution to the meeting "New Developments in Lorentzian Geometry" Berlin, Nov. 20

Scientific paper

Global hyperbolicity is a central concept in Mathematical Relativity. Here, we review the different approaches to this concept explaining both, classical approaches and recent results. The former includes Cauchy hypersurfaces, naked singularities, and the space of the causal curves connecting two events. The latter includes structural results on globally hyperbolic spacetimes, their embeddability in Lorentz-Minkowski, and the recently revised notions of both, causal and conformal boundaries. Moreover, two criteria for checking global hyperbolicity are reviewed. The first one applies to general splitting spacetimes. The second one characterizes accurately global hyperbolicity and spacelike Cauchy hypersurfaces for standard stationary spacetimes, in terms of a naturally associated Finsler metric.

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