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 |
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ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics
Cite this
Lines in space-times. / Eschenburg, J. H.; Galloway, Gregory J.
In: Communications in Mathematical Physics, Vol. 148, No. 1, 08.1992, p. 209-216.Research output: Contribution to journal › Article
}
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 -