Global Existence of Solutions to the Coupled Einstein and Maxwell-Higgs System in the Spherical Symmetry
Abstract.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.
Similar content being viewed by others Explore related subjectsDiscover the latest articles and news from researchers in related subjects, suggested using machine learning. Author information Authors and AffiliationsDepartment of Mathematics, Seoul National University, Seoul 151–742, Korea, e-mail: dhchae@math.snu.ac.kr, Korea
D. Chae
Submitted 18/04/02, accepted 27/11/02
RID="h1"
ID="h1"Communicated by Sergiu Klainerman
About this article Cite this articleChae, D. Global Existence of Solutions to the Coupled Einstein and Maxwell-Higgs System in the Spherical Symmetry. Ann. Henri Poincaré 4, 35–62 (2003). https://doi.org/10.1007/s00023-003-0121-0
Published: 01 March 2003
Issue Date: March 2003
DOI: https://doi.org/10.1007/s00023-003-0121-0
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