Some connections between global hyperbolicity and geodesic completeness

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We establish for space-times obeying certain curvature conditions (consistent with gravity being attractive) some clear cut connections between global hyperbolicity and timelike geodesic completeness. We show, under suitable circumstances, that if the future of a spacelike hypersurface is future timelike geodesically complete then it is global hyperbolic. A partial converse is also obtained. One of our results is a consequence of a ≪splitting theorem≫ for space-times which admit a maximal hypersurface. Our main results are used to improve certain aspects of some splitting theorems previously obtained in the literature.

Original languageEnglish (US)
Pages (from-to)127-141
Number of pages15
JournalJournal of Geometry and Physics
Volume6
Issue number1
DOIs
StatePublished - 1989

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Hyperbolicity
completeness
Geodesic
Completeness
theorems
Space-time
Spacelike Hypersurface
Theorem
Converse
Hypersurface
Gravity
Curvature
curvature
gravitation
Partial

ASJC Scopus subject areas

  • Geometry and Topology
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

Some connections between global hyperbolicity and geodesic completeness. / Galloway, Gregory J.

In: Journal of Geometry and Physics, Vol. 6, No. 1, 1989, p. 127-141.

Research output: Contribution to journalArticle

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