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.
Similar content being viewed by others
References
Abramowitz, M., Stegun, A.I.: Handbook of Mathematical Functions, pp. 331–341. Washington, DC: US National Bureau of Standards, Chap. 8, 1965
Bičák, J., Schmidt, B.: Phys. Rev.D40, 1872 (1989)
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
Chavel, I.: Eigenvalues in Riemannian Geometry. New York: Academic Press 1984
Christodoulou, D.: Commun. Math. Phys.105, 337 (1986),106, 587 (1986),109, 591 (1987);109, 613 (1987)
Christodoulou, D.: Commun Pure Appl. Math.44, 339 (1991)
Christodoulou, D., Klainerman, S.: The Global Nonlinear, Stability of Minkowski Space, preprint (1989)
Chrusciel, P.T.: Commun. Math. Phys.137, 289 (1991)
Chruściel, P. T.: On the global structure of Robinson-Trautman space-times, preprint CMA-R23-90. Proc. R. Soc. London (in press)
Ebin, D.: Proc. Symp. Pure Math. A.M.S.15, 11 (1970)
Fischer, A., Tromba, A.: Math. Ann.237, 311 (1984)
Foster, J.: Proc. Camb. Phil. Soc.66, 521, (1969)
Friedrich, H.: Commun. Math. Phys.107, 587 (1986)
Jenni, F.: Comment. Math. Helv.59, 193 (1984)
Lang, S.: Differential Manifolds. Reading, MA: Addison Wesley 1972
Rendall, A.: Class. Quantum Grav.5, 1339 (1988)
Robinson, I., Trautman, T.: Proc. Roy. Soc. Lond.A265, 463 (1962)
Schmidt, B.: Gen. Rel. Grav20, 65 (1988)
Singleton, D.: PhD Thesis, Monash, University, Melbourne 1989
Singleton, D.: Class. Quantum Grav.7, 1333 (1990)
Tod, P.: Class. Quantum Grav.6, 1159 (1989)
Author information
Authors and Affiliations
Additional information
Communicated by S.-T. Yau
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02099531