Communications in Mathematical Physics

, Volume 26, Issue 2, pp 87–101 | Cite as

Solutions of the Einstein-Maxwell equations with many black holes

  • J. B. Hartle
  • S. W. Hawking


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.


Neural Network Black Hole Statistical Physic Static Equilibrium Complex System 
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Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • J. B. Hartle
    • 1
    • 2
  • S. W. Hawking
    • 1
  1. 1.Institute of Theoretical AstronomyCambridgeEngland
  2. 2.Department of PhysicsUniversity of CaliforniaSanta BarbaraUSA

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