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


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.


Differential Geometry Essential Singularity Spacelike Slice Timelike Congruence Incomplete Curf 
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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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