### 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) |
---|---|

Pages (from-to) | 209-216 |

Number of pages | 8 |

Journal | Communications in Mathematical Physics |

Volume | 148 |

Issue number | 1 |

DOIs | |

State | Published - Aug 1992 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

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

**Lines in space-times.** / Eschenburg, J. H.; Galloway, Gregory J.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 148, no. 1, pp. 209-216. https://doi.org/10.1007/BF02102373

}

TY - JOUR

T1 - Lines in space-times

AU - Eschenburg, J. H.

AU - Galloway, Gregory J

PY - 1992/8

Y1 - 1992/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0039439893&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039439893&partnerID=8YFLogxK

U2 - 10.1007/BF02102373

DO - 10.1007/BF02102373

M3 - Article

AN - SCOPUS:0039439893

VL - 148

SP - 209

EP - 216

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -