Communications in Mathematical Physics

, Volume 26, Issue 2, pp 87–101

Solutions of the Einstein-Maxwell equations with many black holes


  • J. B. Hartle
    • Institute of Theoretical Astronomy
    • Department of PhysicsUniversity of California
  • S. W. Hawking
    • Institute of Theoretical Astronomy

DOI: 10.1007/BF01645696

Cite this article as:
Hartle, J.B. & Hawking, S.W. Commun.Math. Phys. (1972) 26: 87. doi:10.1007/BF01645696


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=G1/2m. 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.

Copyright information

© Springer-Verlag 1972