Annales Henri Poincaré

, Volume 4, Issue 1, pp 35–62 | Cite as

Global Existence of Solutions to the Coupled Einstein and Maxwell-Higgs System in the Spherical Symmetry

Original article


We prove the global unique existence of classical solutions to the Einstein equations coupled with Maxwell-Higgs system for small initial data under the spherical symmetry. We also obtain the decay estimates of the solutions, and find that the corresponding space-time is time-like and null geodesically complete toward the future. For the proof we reduce the system to a single first order integrodifferential equation, and use the contraction mapping theorem in the appropriate function spaces. We also obtain the completeness of space-time along the future directed time-like lines exterior to a region which resembles the even horizon of the Reissner-Nordström black hole.


Black Hole Initial Data Function Space Classical Solution Einstein Equation 


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Copyright information

© Birkhäuser Verlag Basel, 2003

Authors and Affiliations

  • D. Chae
    • 1
  1. 1.Department of Mathematics, Seoul National University, Seoul 151–742, Korea, e-mail:

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