Communications in Mathematical Physics

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

Lines in space-times

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


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.


Neural Network Statistical Physic Complex System Energy Condition Nonlinear Dynamics 
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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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