General Relativity and Gravitation

, Volume 34, Issue 10, pp 1625–1635 | Cite as

The Stability of Abstract Boundary Essential Singularities

  • Michael J. S. L. Ashley


The abstract boundary has, in recent years, proved a general and flexible way to define the singularities of space-time. In this approach an essential singularity is a non-regular boundary point of an embedding which is accessible by a chosen family of curves within finite parameter distance. Ashley and Scott proved the first theorem relating essential singularities in strongly causal space-times to causal geodesic incompleteness. Linking this with the work of Beem on the Cr-stability of geodesic incompleteness allows proof of the stability of these singularities. Here I present this result stating the conditions under which essential singularities are C1-stable against perturbations of the metric.

abstract boundary essential singularity stability space-time 


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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • Michael J. S. L. Ashley
    • 1
  1. 1.Department of Physics and Theoretical Physics, Faculty of ScienceThe Australian National UniversityCanberraAustralia

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