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On the multi-string solutions of the self-dual static Einstein-Maxwell-Higgs system

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Abstract.

In this paper we prove existence and precise decay estimates at infinity of solutions to the Bogomol’nyi system of the static Einstein equations coupled with the Maxwell-Higgs fields with translational symmetry in one direction. The equations model cosmic strings(or superconducting strings) in equilibrium state. The Higgs fields of our solutions, in particular, tend to the symmetric vacuum at infinity. The construction of our solution is by the perturbation type of argument combined with the implicit function theorem.

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Authors and Affiliations

  1. Department of Mathematics, Seoul National University, 151-742, Seoul, Korea

    Dongho Chae

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  1. Dongho Chae
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Correspondence to Dongho Chae.

Additional information

Received: 12 December 2002, Accepted: 12 June 2003, Published online: 4 September 2003

Mathematics Subject Classification (2000):

35J60, 49J40, 58E15

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Chae, D. On the multi-string solutions of the self-dual static Einstein-Maxwell-Higgs system. Cal Var 20, 47–63 (2004). https://doi.org/10.1007/s00526-003-0227-8

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  • DOI: https://doi.org/10.1007/s00526-003-0227-8

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