### Abstract

We construct a complete timelike maximal geodesic ("line") in a timelike geodesically complete spacetime M containing a compact acausal spacelike hypersurface S which lies in the past of some S-ray. An S-ray is a future complete geodesic starting on S which maximizes Lorentzian distance from S to any of its points. If the timelike convergence condition (strong energy condition) holds, a line exists only if M 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.

Original language | English (US) |
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Pages (from-to) | 209-216 |

Number of pages | 8 |

Journal | Communications in Mathematical Physics |

Volume | 148 |

Issue number | 1 |

DOIs | |

State | Published - Aug 1 1992 |

Externally published | Yes |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Eschenburg, J. H., & Galloway, G. J. (1992). Lines in space-times.

*Communications in Mathematical Physics*,*148*(1), 209-216. https://doi.org/10.1007/BF02102373