General Relativity and Gravitation

, Volume 14, Issue 6, pp 609–613 | Cite as

Spatially compact space-times that shrink

  • C. J. S. Clarke
Research Articles

Abstract

A criterion is given under which essential singularities occur in any space-time having compact spacelike slices whose size (measured by a parallelly propagated frame) shrinks to zero, and where there is a timelike congruence with incomplete curves.

Keywords

Differential Geometry Essential Singularity Spacelike Slice Timelike Congruence Incomplete Curf 

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References

  1. 1.
    Clarke, C. J. S. (1975). Singularities in globally hyperbolic space-time,Commun. Math. Phys.,41, 15–78.Google Scholar
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    Clarke, C. J. S. Space-times of low differentiability and singularities,J. Math. Anal. Appl., to appear.Google Scholar
  3. 3.
    Hawking, S. W., and Ellis, G. F. R. (1973). The large scale structure of space-time, Cambridge University Press, Cambridge.Google Scholar
  4. 4.
    Moncrief, V. E. (1981). An infinite dimensional family of vacuum cosmological models with Taub-NUT-type extensions,Phys. Rev. D,23, 312–315.Google Scholar

Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • C. J. S. Clarke
    • 1
  1. 1.Department of MathematicsUniversity of YorkHeslingtonEngland

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