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

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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 languageEnglish (US)
Pages (from-to)79-90
Number of pages12
JournalLetters in Mathematical Physics
Issue number2
StatePublished - Oct 1992


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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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