General Relativity and Gravitation

, Volume 14, Issue 8, pp 793–801 | Cite as

Definitions of black holes without use of the boundary at infinity

  • Andrzej Królak
Research Articles


Two definitions of a black hole are given without reference to the boundary at infinity of of space-time. One definition does not require any global causality condition and the other is applicable to a closed Friedmann-like space-time. The area theorem is found to hold in both cases.


Black Hole Differential Geometry Causality Condition Area Theorem 
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.
    Hawking, S. W., and Ellis, G. F. R. (1973).The Large-Scale Structure of Space-Time, Cambridge University Press, Cambridge.Google Scholar
  2. 2.
    Tipler, F. J. (1977).Nature,270, 500.Google Scholar
  3. 3.
    Tipler, F. J., Clarke, C. J. S., and Ellis, G. F. R. (1980). “Singularities and Horizons-A Review Article,” InGeneral Relativity and Gravitation: One Hundred Years After the Birth of Albert Einstein, A. Held, ed. Plenum Press, New York.Google Scholar
  4. 4.
    Geroch, R., Kronheimer, E. H., and Penrose, R. (1972).Proc. R. Soc. London, Ser. A,327, 545.Google Scholar
  5. 5.
    Penrose, R. (1965).Phys. Rev. Lett.,14, 57.Google Scholar
  6. 6.
    Penrose, R. (1974). InConfrontation of Cosmological Theories with Observational Data, IAU Symposium No. 63, D. Reidel, Dordrecht.Google Scholar
  7. 7.
    Wheeler, J. A. (1975). InQuantum Gravity-An Oxford Symposium, ed. Isham, C. J., Clarendon Press, Oxford.Google Scholar
  8. 8.
    Penrose, R. (1978). “Techniques of Differential Topology in Relativity,” Department of Mathematics, University of Pittsburgh.Google Scholar
  9. 9.
    Lee, C. W. (1978).Nature,275, 725.Google Scholar

Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • Andrzej Królak
    • 1
  1. 1.Instytut Fizyki TeoretycznejWarszawaPoland

Personalised recommendations