### Abstract

This paper establishes the existence of regular stationary solutions of the coupled Einstein-matter-gauge equations with a cylindrical symmetry. Such solutions are called cosmic strings or gravitational vortices and are believed to have important implications in cosmology and quantum physics. It is shown that for a prescribed string location with a string or winding number below an explicit barrier, the system possesses a continuous family of distinct finite-energy solution configurations. The proof of the main existence theorem relies on a special shooting method. Power-type decay estimates at spatial infinity are also obtained.

Original language | English (US) |
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Pages (from-to) | 160-190 |

Number of pages | 31 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 195 |

Issue number | 1 |

DOIs | |

State | Published - Oct 1 1995 |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

**Regular Stationary Solutions of the Cylindrically Symmetric Einstein-Matter-Gauge Equations.** / Spruck, J.; Yang, Y. S.

Research output: Contribution to journal › Article

*Journal of Mathematical Analysis and Applications*, vol. 195, no. 1, pp. 160-190. https://doi.org/10.1006/jmaa.1995.1349

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TY - JOUR

T1 - Regular Stationary Solutions of the Cylindrically Symmetric Einstein-Matter-Gauge Equations

AU - Spruck, J.

AU - Yang, Y. S.

PY - 1995/10/1

Y1 - 1995/10/1

N2 - This paper establishes the existence of regular stationary solutions of the coupled Einstein-matter-gauge equations with a cylindrical symmetry. Such solutions are called cosmic strings or gravitational vortices and are believed to have important implications in cosmology and quantum physics. It is shown that for a prescribed string location with a string or winding number below an explicit barrier, the system possesses a continuous family of distinct finite-energy solution configurations. The proof of the main existence theorem relies on a special shooting method. Power-type decay estimates at spatial infinity are also obtained.

AB - This paper establishes the existence of regular stationary solutions of the coupled Einstein-matter-gauge equations with a cylindrical symmetry. Such solutions are called cosmic strings or gravitational vortices and are believed to have important implications in cosmology and quantum physics. It is shown that for a prescribed string location with a string or winding number below an explicit barrier, the system possesses a continuous family of distinct finite-energy solution configurations. The proof of the main existence theorem relies on a special shooting method. Power-type decay estimates at spatial infinity are also obtained.

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UR - http://www.scopus.com/inward/citedby.url?scp=0345475361&partnerID=8YFLogxK

U2 - 10.1006/jmaa.1995.1349

DO - 10.1006/jmaa.1995.1349

M3 - Article

AN - SCOPUS:0345475361

VL - 195

SP - 160

EP - 190

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -