Communications in Mathematical Physics

, Volume 290, Issue 1, pp 239–248 | Cite as

K-Causality Coincides with Stable Causality

  • E. MinguzziEmail author


It is proven that K-causality coincides with stable causality, and that in a K-causal spacetime the relation K + coincides with the Seifert’s relation. As a consequence the causal relation “the spacetime is strongly causal and the closure of the causal relation is transitive” stays between stable causality and causal continuity.


Causal Relation Light Cone Compact Closure Causal Curve Global Hyperbolicity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Akolia G.M., Joshi P., Vyas U.: On almost causality. J. Math. Phys. 22, 1243–1247 (1981)CrossRefADSMathSciNetGoogle Scholar
  2. 2.
    Bernal A.N., Sánchez M.: Globally hyperbolic spacetimes can be defined as ‘causal’ instead of ‘strongly causal’. Class. Quant. Grav. 24, 745–749 (2007)zbMATHCrossRefADSGoogle Scholar
  3. 3.
    Dowker H.F., Garcia R.S., Surya S.: K-causality and degenerate spacetimes. Class. Quant. Grav. 17, 4377–4396 (2000)zbMATHCrossRefADSMathSciNetGoogle Scholar
  4. 4.
    Hawking S.W., Ellis G.F.R.: The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge (1973)zbMATHGoogle Scholar
  5. 5.
    Hawking S.W., Sachs R.K.: Causally continuous spacetimes. Commun. Math. Phys. 35, 287–296 (1974)CrossRefADSMathSciNetGoogle Scholar
  6. 6.
    Janardhan S., Saraykar R.V.: K-causal structure of space-time in general relativity. Pramana-Journal of Physics 70, 587–601 (2008)CrossRefADSGoogle Scholar
  7. 7.
    Minguzzi E.: The causal ladder and the strength of K-causality. I. Class. Quant. Grav. 25, 015009 (2008)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Minguzzi E.: The causal ladder and the strength of K-causality. II. Class. Quant. Grav. 25, 015010 (2008)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Minguzzi, E.: Chronological spacetimes without lightlike lines are stably causal. Preprint: available at[gr-qc], 2008, to appear in Commun. Math. Phys. doi: 10.1007/s00220-009-0784-6
  10. 10.
    Minguzzi E.: Limit curve theorems in Lorentzian geometry. J. Math. Phys. 49, 092501 (2008)CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    Minguzzi E.: Non-imprisonment conditions on spacetime. J. Math. Phys. 49, 062503 (2008)CrossRefADSMathSciNetGoogle Scholar
  12. 12.
    Minguzzi E.: Weak distinction and the optimal definition of causal continuity. Class. Quant. Grav. 25, 075015 (2008)CrossRefADSMathSciNetGoogle Scholar
  13. 13.
    Minguzzi, E., Sánchez, M.: The causal hierarchy of spacetimes. In: Baum, H., Alekseevsky, D. (eds.), Recent developments in pseudo-Riemannian geometry, of ESI Lect. Math. Phys., Zurich: Eur. Math. Soc. Publ. House, 2008, pp. 299–358Google Scholar
  14. 14.
    Seifert H.: The causal boundary of space-times. Gen. Rel. Grav. 1, 247–259 (1971)zbMATHCrossRefADSMathSciNetGoogle Scholar
  15. 15.
    Senovilla J.M.M.: Singularity theorems and their consequences. Gen. Rel. Grav. 30, 701–848 (1998)zbMATHCrossRefADSMathSciNetGoogle Scholar
  16. 16.
    Sorkin R.D., Woolgar E.: A causal order for spacetimes with C 0 Lorentzian metrics: proof of compactness of the space of causal curves. Class. Quant. Grav. 13, 1971–1993 (1996)zbMATHCrossRefADSMathSciNetGoogle Scholar
  17. 17.
    Woodhouse N.M.J.: The differentiable and causal structures of space-time. J. Math. Phys. 14, 495–501 (1973)zbMATHCrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Dipartimento di Matematica ApplicataUniversità degli Studi di FirenzeFirenzeItaly

Personalised recommendations