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Communications in Mathematical Physics

, Volume 148, Issue 1, pp 209–216 | Cite as

Lines in space-times

  • J. -H. Eschenburg
  • G. J. Galloway
Article

Abstract

We construct a complete timelike maximal geodesic (“line”) in a timelike geodesically complete spacetimeM containing a compact acausal spacelike hypersurfaceS which lies in the past of someS-ray. AnS-ray is a future complete geodesic starting onS which maximizes Lorentzian distance fromS to any of its points. If the timelike convergence condition (strong energy condition) holds, a line exists only ifM is static, i.e. it splits geometrically as space × time. So timelike completeness must fail for a nonstatic spacetime with strong energy condition which contains a “closed universe”S with the above properties.

Keywords

Neural Network Statistical Physic Complex System Energy Condition Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • J. -H. Eschenburg
    • 1
  • G. J. Galloway
    • 2
  1. 1.Institut für MathematikUniversität AugsburgAugsburgFRG
  2. 2.Department of Mathematics and Computer SciencesCoral GablesUSA

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