Lines in space-times

J. H. Eschenburg; G. J. Galloway

doi:10.1007/BF02102373

Lines in space-times

J. H. Eschenburg, G. J. Galloway

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

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	https://doi.org/10.1007/BF02102373
State	Published - Aug 1 1992
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF02102373

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PY - 1992/8/1

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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.

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JF - Communications in Mathematical Physics

SN - 0010-3616

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Lines in space-times

Abstract

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