Communications in Mathematical Physics

, Volume 25, Issue 2, pp 152–166 | Cite as

Black holes in general relativity

  • S. W. Hawking


It is assumed that the singularities which occur in gravitational collapse are not visible from outside but are hidden behind an event horizon. This means that one can still predict the future outside the event horizon. A black hole on a spacelike surface is defined to be a connected component of the region of the surface bounded by the event horizon. As time increase, black holes may merge together but can never bifurcate. A black hole would be expected to settle down to a stationary state. It is shown that a stationary black hole must have topologically spherical boundary and must be axisymmetric if it is rotating. These results together with those of Israel and Carter go most of the way towards establishing the conjecture that any stationary black hole is a Kerr solution. Using this conjecture and the result that the surface area of black holes can never decrease, one can place certain limits on the amount of energy that can be extracted from black holes.


Neural Network Black Hole Statistical Physic General Relativity Complex System 
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  1. 1.
    Penrose, R.: Phys. Rev. Letters14, 57 (1965).Google Scholar
  2. 2.
    —— In: de Witt, C.M., Wheeler, J.A. (Eds.): Battelle Rencontres (1967). New York: Benjamin 1968.Google Scholar
  3. 3.
    Hawking, S.W., Ellis, G.F.R.: The large scale structure of space time. Cambridge: Cambridge University Press (to be published).Google Scholar
  4. 4.
    —— Penrose, R.: Proc. Roy. Soc. A314, 529 (1970).Google Scholar
  5. 5.
    Penrose, R.: Seminar at Cambridge University, January 1971 (unpublished).Google Scholar
  6. 6.
    Gibbons, G.W., Penrose, R.: To be published.Google Scholar
  7. 7.
    Geroch, R.P.: J. Math. Phys.11, 437 (1970).Google Scholar
  8. 8.
    Israel, W.: Phys. Rev.164, 1776 (1967).Google Scholar
  9. 9.
    Carter, B.: Phys. Rev. Letters26, 331 (1971).Google Scholar
  10. 10.
    —— Phys. Rev.174, 1559 (1968).Google Scholar
  11. 11.
    Müller zum Hagen, H.: Proc. Cambridge Phil. Soc.68, 199 (1970).Google Scholar
  12. 12.
    Carter, B.: Commun. math. Phys.17, 233 (1970).Google Scholar
  13. 13.
    Newman, E.T., Penrose, R.: J. Math. Phys.3, 566 (1962).Google Scholar
  14. 14.
    Hawking, S.W.: Proc. Roy. Soc. A300, 187 (1967).Google Scholar
  15. 15.
    Sachs, R.K.: J. Math. Phys.3, 908 (1962).Google Scholar
  16. 16.
    Penrose, R.: Characteristic initial data for zero rest mass including gravitation, preprint (1961).Google Scholar
  17. 17.
    Carter, B.: J. Math. Phys.10, 70 (1969).Google Scholar
  18. 18.
    Israel, W.: Commun. math. Phys.8, 245 (1968).Google Scholar
  19. 19.
    Lichnerowicz, A.: Théories relativistes de la gravitation et de l'électromagnétisme. Paris: Masson 1955.Google Scholar
  20. 20.
    Penrose, R.: Nuovo Cimento Serie 1,1, 252 (1969).Google Scholar
  21. 21.
    Newman, E.T., Penrose, R.: J. Math. Phys.7, 863 (1966).Google Scholar
  22. 22.
    Christodoulou, D.: Phys. Rev. Letters25, 1596 (1970).Google Scholar
  23. 23.
    Penrose, R.: Phys. Rev. Letters10, 66 (1963).Google Scholar
  24. 24.
    Hartle, J.B., Hawking, S.W.: Commun. math. Phys. To be published.Google Scholar
  25. 25.
    Hawking, S.W.: Commun. math. Phys.18, 301 (1970).Google Scholar

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • S. W. Hawking
    • 1
  1. 1.Institute of Theoretical AstronomyUniversity of CambridgeCambridgeEngland

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