### Abstract

String-like static solutions of the Einstein matter-gauge equations have interesting implications in cosmology. It has been shown recently that, at a critical coupling phase, this system of equations allows a reduction into a coupled Einstein-Bogomol'nyi system. In this Letter, we prove that, in the important case where the underlying two-dimensional Riemannian manifold is either compact or asymptotically Euclidean, the two systems are actually equivalent. Moreover, we show that the standard assumption that the strings reside in a conformally Euclidean surface will give us a metric which fails to be asymptotically Euclidean. In particular, in the radially symmetric case, we establish under the finite energy condition the boundary behavior of the metric. These results may indicate that a string solution will inevitably lead to nonflatness of the space at infinity even on the cross-section.

Original language | English (US) |
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Pages (from-to) | 79-90 |

Number of pages | 12 |

Journal | Letters in Mathematical Physics |

Volume | 26 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1992 |

### Fingerprint

### Keywords

- Mathematics Subject Classifications (1991): 58G03, 83F05, 81T20

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

**An equivalence theorem for string solutions of the Einstein matter-gauge equations.** / Yang, Yisong.

Research output: Contribution to journal › Article

*Letters in Mathematical Physics*, vol. 26, no. 2, pp. 79-90. https://doi.org/10.1007/BF00398804

}

TY - JOUR

T1 - An equivalence theorem for string solutions of the Einstein matter-gauge equations

AU - Yang, Yisong

PY - 1992/10

Y1 - 1992/10

N2 - String-like static solutions of the Einstein matter-gauge equations have interesting implications in cosmology. It has been shown recently that, at a critical coupling phase, this system of equations allows a reduction into a coupled Einstein-Bogomol'nyi system. In this Letter, we prove that, in the important case where the underlying two-dimensional Riemannian manifold is either compact or asymptotically Euclidean, the two systems are actually equivalent. Moreover, we show that the standard assumption that the strings reside in a conformally Euclidean surface will give us a metric which fails to be asymptotically Euclidean. In particular, in the radially symmetric case, we establish under the finite energy condition the boundary behavior of the metric. These results may indicate that a string solution will inevitably lead to nonflatness of the space at infinity even on the cross-section.

AB - String-like static solutions of the Einstein matter-gauge equations have interesting implications in cosmology. It has been shown recently that, at a critical coupling phase, this system of equations allows a reduction into a coupled Einstein-Bogomol'nyi system. In this Letter, we prove that, in the important case where the underlying two-dimensional Riemannian manifold is either compact or asymptotically Euclidean, the two systems are actually equivalent. Moreover, we show that the standard assumption that the strings reside in a conformally Euclidean surface will give us a metric which fails to be asymptotically Euclidean. In particular, in the radially symmetric case, we establish under the finite energy condition the boundary behavior of the metric. These results may indicate that a string solution will inevitably lead to nonflatness of the space at infinity even on the cross-section.

KW - Mathematics Subject Classifications (1991): 58G03, 83F05, 81T20

UR - http://www.scopus.com/inward/record.url?scp=34249843115&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249843115&partnerID=8YFLogxK

U2 - 10.1007/BF00398804

DO - 10.1007/BF00398804

M3 - Article

AN - SCOPUS:34249843115

VL - 26

SP - 79

EP - 90

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 2

ER -