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Remarks on the notion of global hyperbolicity

Published online by Cambridge University Press:  30 September 2008

M. Sánchez
Affiliation:
Dep. Geometría y Topología, Fac. Ciencias, Campus Fuentenueva s/n, 18071 Granada, Spain
U. Granada
Affiliation:
Dep. Geometría y Topología, Fac. Ciencias, Campus Fuentenueva s/n, 18071 Granada, Spain
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Abstract

Global hyperbolicity is a classical and well-known concept, which lies in the core of General Relativity. Here we discuss briefly five approaches to this concept. They yield different definitions which become natural in diverse contexts: the initial value problem, singularity theorems, existence of maximizing causal geodesics, possibility to split globally the spacetime, causal boundaries. The neat formulation and definitive equivalence between these definitions have been completed only recently. A very brief summary is presented.

Type
Research Article
Copyright
© EAS, EDP Sciences, 2008

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