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Remarks on the notion of global hyperbolicity

Published online by Cambridge University Press:  30 September 2008

A. Oscoz ,
E. Mediavilla ,
M. Serra-Ricart ,
M. Sánchez  and
U. Granada
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, whichlies in the core of General Relativity. Here we discuss brieflyfive approaches to this concept. They yield different definitionswhich become natural in diverse contexts: the initial valueproblem, singularity theorems, existence of maximizing causalgeodesics, possibility to split globally the spacetime, causalboundaries. The neat formulation and definitive equivalencebetween these definitions have been completed only recently. Avery brief summary is presented.

Type
Research Article
Information
European Astronomical Society Publications Series , Volume 30: Spanish Relativity Meeting - Encuentros Relativistas Españoles, ERE2007: Relativistic Astrophysics and Cosmology , 2008 , pp. 201 - 204
Copyright
© EAS, EDP Sciences, 2008

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References

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