Skip to main content

“Topological Censorship” is not proven


I show that there is a significant lacuna in the proof of the theorem known as “Topological Censorship” (a theorem forbidding a solution of Einstein’s equations to have some topological features, such as traversable wormholes, without violating the averaged null energy condition). To fill the lacuna one would probably have to revise the class of spacetimes for which the theorem is formulated.

This is a preview of subscription content, access via your institution.


  1. J. L. Friedman, K. Schleich, and D. M. Witt, Phys. Rev. Lett. 71, 1486 (1993); Erratum: Phys. Rev. Lett. 75, 1872 (1995).

    MathSciNet  ADS  Article  Google Scholar 

  2. R. Geroch and G. T. Horowitz. In: S. W. Hawking and W. Israel (eds.), General Relativity, an Einstein Centenary Survey (Cambridge Univ. Press, New York, 1979), p. 212.

  3. P. T. Chruściel and R. M. Wald, Class.Quantum Grav. 11, L147 (1994).

    Article  Google Scholar 

  4. G. J. Galloway, Class. Quantum Grav. 12, L99 (1995).

    MathSciNet  ADS  MATH  Article  Google Scholar 

  5. T. Jacobson and S. Venkataramani, Class. Quantum Grav. 12, 1055 (1995).

    MathSciNet  ADS  MATH  Article  Google Scholar 

  6. M. S. Morris and K. S. Thorne, Am. J. Phys. 56, 395 (1988).

    MathSciNet  ADS  Article  Google Scholar 

  7. S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Spacetime (Cambridge Univ. Press, Cambridge, 1973).

    Book  Google Scholar 

  8. P. T. Chruściel, G. J. Galloway, and D. Solis, Topological Censorship for Kaluza-Klein Space-Times, Arxiv: 0808.3233.

  9. P. T. Chruściel, private communication.

  10. A. Borde, Class. Quantum Grav. 4, 343 (1987).

    MathSciNet  ADS  MATH  Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to S. V. Krasnikov.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Krasnikov, S.V. “Topological Censorship” is not proven. Gravit. Cosmol. 19, 54–56 (2013).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Null Geodesic
  • Null Energy Condition
  • Weak Energy Condition
  • Traversable Wormhole
  • Simple Space