Lines in space-times
- 60 Downloads
We construct a complete timelike maximal geodesic (“line”) in a timelike geodesically complete spacetimeM containing a compact acausal spacelike hypersurfaceS which lies in the past of someS-ray. AnS-ray is a future complete geodesic starting onS which maximizes Lorentzian distance fromS to any of its points. If the timelike convergence condition (strong energy condition) holds, a line exists only ifM 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.
KeywordsNeural Network Statistical Physic Complex System Energy Condition Nonlinear Dynamics
Unable to display preview. Download preview PDF.
- [BE] Beem, J.K., Ehrlich, P.E.: Global Lorentzian geometry, Pure Appl. Math. New York: Dekker 1981Google Scholar
- [E] Eschenburg, J.-H.: The splitting theorem for space-times with strong energy conditions. J. Differ. Geom.27, 477–491 (1988)Google Scholar
- [G2] Galloway, G.J.: Curvature, causality and completeness in space-times with causally complete spacelike slices. Math. Proc. Camb. Phil. Soc.99, 367–375 (1986)Google Scholar
- [HE] Hawking, S.W., Ellis, G.F.R.: The large scale structure of space-time. Cambridge: Cambridge University Press 1973Google Scholar
- [N] Newman, R.P.A.C.: A proof of the splitting conjecture of S.-T. Yau. J. Differ. Geom.31, 163–184 (1990)Google Scholar