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Non-smoothness of event horizons of Robinson-Trautman black holes

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Abstract

It is shown that generic “small data” Robinson-Trautman space-times cannot beC 123 extended beyond the “r=2m Schwarzschild-like” event horizon. This implies that an observer living in such a space-time can determine by local measurements whether or not he has crossed the event-horizon of the black-hole.

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References

  1. Abramowitz, M., Stegun, A.I.: Handbook of Mathematical Functions, pp. 331–341. Washington, DC: US National Bureau of Standards, Chap. 8, 1965

    Google Scholar 

  2. Bičák, J., Schmidt, B.: Phys. Rev.D40, 1872 (1989)

    Google Scholar 

  3. Bourguignon, J.-P.: Comp. Math.30, 1 (1975); Fischer, A.: The Theory of Superspace. In: Relativity: Proceedings of the Relativity Conference in the Midwest, Carmeli, M., Fickler, S.I., Witten, L. (eds.). New York: Plenum Press, 1970

    Google Scholar 

  4. Chavel, I.: Eigenvalues in Riemannian Geometry. New York: Academic Press 1984

    Google Scholar 

  5. Christodoulou, D.: Commun. Math. Phys.105, 337 (1986),106, 587 (1986),109, 591 (1987);109, 613 (1987)

    Article  Google Scholar 

  6. Christodoulou, D.: Commun Pure Appl. Math.44, 339 (1991)

    Google Scholar 

  7. Christodoulou, D., Klainerman, S.: The Global Nonlinear, Stability of Minkowski Space, preprint (1989)

  8. Chrusciel, P.T.: Commun. Math. Phys.137, 289 (1991)

    Google Scholar 

  9. Chruściel, P. T.: On the global structure of Robinson-Trautman space-times, preprint CMA-R23-90. Proc. R. Soc. London (in press)

  10. Ebin, D.: Proc. Symp. Pure Math. A.M.S.15, 11 (1970)

    Google Scholar 

  11. Fischer, A., Tromba, A.: Math. Ann.237, 311 (1984)

    Article  Google Scholar 

  12. Foster, J.: Proc. Camb. Phil. Soc.66, 521, (1969)

    Google Scholar 

  13. Friedrich, H.: Commun. Math. Phys.107, 587 (1986)

    Article  Google Scholar 

  14. Jenni, F.: Comment. Math. Helv.59, 193 (1984)

    Google Scholar 

  15. Lang, S.: Differential Manifolds. Reading, MA: Addison Wesley 1972

    Google Scholar 

  16. Rendall, A.: Class. Quantum Grav.5, 1339 (1988)

    Article  Google Scholar 

  17. Robinson, I., Trautman, T.: Proc. Roy. Soc. Lond.A265, 463 (1962)

    Google Scholar 

  18. Schmidt, B.: Gen. Rel. Grav20, 65 (1988)

    Article  Google Scholar 

  19. Singleton, D.: PhD Thesis, Monash, University, Melbourne 1989

  20. Singleton, D.: Class. Quantum Grav.7, 1333 (1990)

    Article  Google Scholar 

  21. Tod, P.: Class. Quantum Grav.6, 1159 (1989)

    Article  Google Scholar 

Download references

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Author notes

  1. Piotr T. Chruściel

    Present address: Centre for Mathematics and its Applications of the ANU, G.P.O. Box 4, 2601, Canberra, A.C.T., Australia

  2. David B. Singleton

    Present address: Institute of Mathematics, Polish Academy of Sciences, Warsaw

Authors and Affiliations

  1. Australian National University, G.P.O. Box 4, 2601, Canberra, A.C.T., Australia

    Piotr T. Chruściel & David B. Singleton

  2. Institute of Mathematics, Polish Academy of Sciences, G.P.O. Box 4, 2601, Warsaw, A.C.T., Australia

    Piotr T. Chruściel

Authors
  1. Piotr T. Chruściel
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  2. David B. Singleton
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Communicated by S.-T. Yau

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Chruściel, P.T., Singleton, D.B. Non-smoothness of event horizons of Robinson-Trautman black holes. Commun.Math. Phys. 147, 137–162 (1992). https://doi.org/10.1007/BF02099531

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  • DOI: https://doi.org/10.1007/BF02099531

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