Skip to main content
SpringerLink
Log in

Solutions of the Einstein-Maxwell equations with many black holes

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

In Newtonian gravitational theory a system of point charged particles can be arranged in static equilibrium under their mutual gravitational and electrostatic forces provided that for each particle the charge,e, is related to the mass,m, bye=G 1/2 m. Corresponding static solutions of the coupled source free Einstein-Maxwell equations have been given by Majumdar and Papapetrou. We show that these solutions can be analytically extended and interpreted as a system of charged black holes in equilibrium under their gravitational and electrical forces.

We also analyse some of stationary solutions of the Einstein-Maxwell equations discovered by Israel and Wilson. If space is asymptotically Euclidean we find that all of these solutions have naked singularities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Majumdar, S. D.: Phys. Rev.72, 930 (1947).

    Google Scholar 

  2. Papapetrou, A.: Proc. Roy. Irish Acad.A 51, 191 (1947).

    Google Scholar 

  3. Das, A.: Proc. Roy. Soc.A 267, 1 (1962).

    Google Scholar 

  4. Kruskal, M.: Phys. Rev.119, 1742 (1960).

    Google Scholar 

  5. Graves, J., Brill, D.: Phys. Rev.120, 1507 (1960).

    Google Scholar 

  6. Boyer, R. H., Lindquist, R. W.: J. Math. Phys.8, 265 (1967).

    Google Scholar 

  7. Carter, B.: Phys. Rev.174, 1559 (1968).

    Google Scholar 

  8. Israel, W., Wilson, G. A. (to be published).

  9. Carter, B.: Phys. Letters21, 423 (1966).

    Google Scholar 

  10. Kellog, O. D.: Foundations of potential theory. Frederick Ungar, p. 270.

  11. Hawking, S. (to be published).

  12. Newman, E., Couch, E., Chinnapared, K., Exton, A., Prakash, A., Torrence, R.: J. Math. Phys.6, 918 (1965).

    Google Scholar 

  13. Newman, E., Tamborino, L., Unti, T.: J. Math. Phys.4, 915 (1963).

    Google Scholar 

  14. Brill, D.: Phys. Rev.133, 13845 (1964).

    Google Scholar 

  15. Misner, C.: J. Math. Phys.4, 924 (1965).

    Google Scholar 

  16. —— Taub, A.: Zh. Eksp. Theor. Fiz,55, 233 (1968) Soviet-Phys. JETP,28, 122 (1969).

    Google Scholar 

  17. Landau, L., Lifshitz, E. M.: Classical Theory of Fields. Oxford: Pergamon Press 1962.

    Google Scholar 

  18. Israel, W.: Commun. math. Phys.8, 245 (1968).

    Google Scholar 

  19. Carter, B.: Phys. Rev. Letters26, 331 (1971).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Theoretical Astronomy, Cambridge, England

    J. B. Hartle & S. W. Hawking

  2. Department of Physics, University of California, 93 106, Santa Barbara, California, USA

    J. B. Hartle

Authors
  1. J. B. Hartle
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. W. Hawking
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Alfred P. Sloan Research Fellow, supported in part by the National Science Foundation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hartle, J.B., Hawking, S.W. Solutions of the Einstein-Maxwell equations with many black holes. Commun.Math. Phys. 26, 87–101 (1972). https://doi.org/10.1007/BF01645696

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01645696

Keywords

Search

Navigation