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 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