Advertisement

International Journal of Theoretical Physics

, Volume 42, Issue 7, pp 1671–1676 | Cite as

Stability of Cauchy Horizons

  • Robert J. Budzyński
  • Witold Kondracki
  • Andrzej Królak
Article
  • 31 Downloads

Abstract

We prove that for any 3-dimensional compact hypersurface S in a noncompact 4-dimensional space-time manifold M, SM, the set of Lorentzian metrics on M for which S is a partial Cauchy surface and Cauchy horizon of S is nonempty contains a nonempty open subset (in compact-open topology). This result indicates that the set of metrics admitting Cauchy horizons originating from compact hypersurfaces is large.

spacetime geometry general relativity Cauchy horizons 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. Beem, J. K. (1995). Causality and Cauchy horizons. General Relativity and Gravitation 27, 93-108.Google Scholar
  2. Beem, J. K., Ehrlich, P. E., and Easley, K. L. (1996). Global Lorentzian Geometry, 2nd edn., Marcel Dekker, New York. Pure and Applied Mathematics Vol. 202.Google Scholar
  3. Chruściel, P. T. and Isenberg, J. (1997). On the stability of differentiability of Cauchy horizons. Communications in Analysis and Geometry 5, 249-277.Google Scholar
  4. Hawking, S. W. and Ellis, G. F. R. (1973). The Large Scale Structure of Space-time, Cambridge University Press, Cambridge.Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • Robert J. Budzyński
    • 1
  • Witold Kondracki
    • 2
  • Andrzej Królak
    • 2
  1. 1.Department of PhysicsWarsaw UniversityWarsawPoland
  2. 2.Polish Academy of SciencesInstitute of MathematicsWarsawPoland

Personalised recommendations