Advertisement

General Relativity and Gravitation

, Volume 9, Issue 7, pp 597–619 | Cite as

A comment on the uniqueness theorems for stationary black holes

  • Michael Streubel
Research Articles
  • 42 Downloads

Abstract

A simple local geometric condition is given that is sufficient to restrict the possible variety of exterior fields of all stationary axisymmetric black hole spaces to depend only on a finite number of parameters. It is discussed how this condition could be used to gain insight into the nature of the Carter-Robinson uniqueness theorem. Also a new coordinate system is constructed for all stationary axially symmetric space-times possessing a bifurcate Killing horizon. It covers a whole neighborhood of the horizons and of the bifurcation axis and possesses special geometric properties that are easy to visualize. The Kerr metric together with its spin coefficients and Weyl tensor components are described in the new coordinates.

Keywords

Black Hole Coordinate System Finite Number Geometric Property Differential Geometry 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Israel, W. (1967).Phys. Rev.,164, 1776.Google Scholar
  2. 2.
    Carter, B. (1973). “The General Theory of Stationary Black Hole States,” inBlack Holes, ed. De Witt and De Witt (Gordon and Breach, New York).Google Scholar
  3. 3.
    Hawking, S. W., and Ellis, G. F. R. (1973).The Large Scale Structure of Spacetime (Cambridge University Press, London).Google Scholar
  4. 4.
    Robinson, D. C. (1975).Phys. Rev. Lett.,34, 905.Google Scholar
  5. 5.
    Israel, W. (1973).Lett. Nuov. Cim.,6, 267.Google Scholar
  6. 6.
    Hájíček, P. (1973).Commun. Math. Phys.,34, 53.Google Scholar
  7. 7.
    Müller zum Hagen, H., and Seifert, H. J. (1976). Preprint, Hamburg.Google Scholar
  8. 8.
    Carter, B. (1972).The Stationary Axisymmetric Black Hole Problem, Cambridge University preprint.Google Scholar
  9. 9.
    Hájíček, P., and Schmidt, B. G. (1976). Private communication.Google Scholar
  10. 10.
    Boyer, R. H. (1969).Proc. R. Soc. London A,311, 245.Google Scholar
  11. 11.
    Carter, B. (1969).J. Math. Phys.,10, 70.Google Scholar
  12. 12.
    Hájíček, P. (1973).Commun. Math. Phys.,34, 37.Google Scholar
  13. 13.
    Carter, B. (1970).Commun. Math. Phys.,17, 233.Google Scholar
  14. 14.
    Müller zum Hagen, H., and Seifert, H. J. (1973). “Two Axisymmetric Black Holes cannot be in Static Equilibrium,” University of Hamburg, preprint.Google Scholar
  15. 15.
    Müller zum Hagen, H. (1970).Proc. Cambridge Phil. Soc.,68, 199.Google Scholar
  16. 16.
    Bardeen, J. M., Carter, B., and Hawking, S. W. (1973).Commun. Math. Phys.,31, 161.Google Scholar
  17. 17.
    Pajerski, D., and Newman, E. T. (1971).J. Math. Phys.,12, 1929.Google Scholar
  18. 18.
    Israel, W. (1966).Phys. Rev.,143, 1016.Google Scholar
  19. 19.
    Miller, J. G. (1975).J. Math. Phys.,14, 486.Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • Michael Streubel
    • 1
  1. 1.Max-Planck-Institute for AstrophysicsMünchen 40West Germany

Personalised recommendations