Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-28T14:51:52.105Z Has data issue: false hasContentIssue false
  • English
  • Français

On the geodesic completeness of causal space-times

Published online by Cambridge University Press:  24 October 2008

C. J. S. Clarke
C. J. S. Clarke
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge.
Get access Rights & Permissions [Opens in a new window]

Abstract

A geodesic in space-time is complete if it can be extended to infinite values of its affine parameter: it is shown that all strongly causal spaces are conformal to space-times in which all null geodesies are complete, and that a wide class of space-times are conformal to ones in which almost no null geodesies are complete.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 69 , Issue 2 , March 1971 , pp. 319 - 323
Copyright
Copyright © Cambridge Philosophical Society 1971

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Kronheimer, E. H. and Penrose, R.Proc. Cambridge Philos. Soc. 63 (1967), 481.CrossRefGoogle Scholar
(2)Penrose, R. Conformal treatment of infinity, in Relativity groups and topology. Eds. De Witt, C. and De Witt, B., Gordon, and Breach, (London, 1963)Google Scholar
(3)Hawking, S. W.Proc. Hoy. Soc. Ser. A 308 (1969), 433.Google Scholar
(4)Seitert, H.-J. Doctoral thesis at University of Hamburg (1968).Google Scholar
(5)Steenrod, N.The topology of fibre bundles (Princeton University Press, 1951).CrossRefGoogle Scholar
(6)Hawking, S. W.Proc. Roy. Soc. Ser. A 300 (1968), 187.Google Scholar
(7)Nagata, J.-I.Modern dimension theory (Amsterdam, 1965)Google Scholar
(8)Geroch, R. J.Mathematical Phys. 9 (1968), 450.CrossRefGoogle Scholar
(9)Schmidt, B. G.A new definition of singularities in general relativity, in Proceedings of the Gwatt seminar on topology and its bearings on general relativity (to appear).Google Scholar
(10)Kobayashi, S. and Nominzu, K.Foundations of differential geometry (Interscience; London, 1963).Google Scholar
(11)Geroch, R. J.Mathematical Phys. 9 (1968), 1739.CrossRefGoogle Scholar