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Classification of String Solutions for the Self-Dual Einstein–Maxwell–Higgs Model

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Abstract

In this paper, we are concerned with an elliptic system arising from the Einstein–Maxwell–Higgs model which describes electromagnetic dynamics coupled with gravitational fields in spacetime. Reducing this system to a single equation and setting up the radial ansatz, we classify solutions into three cases: topological solutions, nontopological solutions of type I, and nontopological solutions of type II. There are two important constants: \(a>0\) representing the gravitational constant and \(N\ge 0\) representing the total string number. When \(0\le aN<2\), we give a complete classification of all possible solutions and prove the uniqueness of solutions for a given decay rate. In particular, we obtain a new class of topological solitons, with nonstandard asymptotic value \(\sigma <0\) at infinity, when the total string number is sufficiently large such that \(1<aN<2\). We also prove the multiple existence of solutions for a given decay rate in the case \(aN \ge 2\). Our classification improves previous results which are known only for the case \(0<aN<1\).

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Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2015R1D1A1A01057499).

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Authors and Affiliations

  1. Department of Mathematics, Kyung Hee University, Seoul, 130-701, Korea

    Jongmin Han & Juhee Sohn

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  1. Jongmin Han
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  2. Juhee Sohn
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Correspondence to Jongmin Han.

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Communicated by Mihalis Dafermos.

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Han, J., Sohn, J. Classification of String Solutions for the Self-Dual Einstein–Maxwell–Higgs Model. Ann. Henri Poincaré 20, 1699–1751 (2019). https://doi.org/10.1007/s00023-019-00788-1

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