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I searched on the internet superficially but I couldn't find it.

Is there any reference that find the solution to Einstein's Field Equations for a rotating Cosmic String?

Personally haven't got the time to do the computation for the rotating flux tube extension of a 2d vortex solution to the Higgsed-$U(1)$ Yang Mills, but that's where I would definitely start from.

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  • $\begingroup$ A rotating string of what shape? Straight? Circular? Which axis is it rotating around? $\endgroup$
    – Ghoster
    Commented Mar 28 at 16:27
  • $\begingroup$ I'd say since I am interested in the local behavior, you can take the infinitly long straight line for granted. @Ghoster $\endgroup$ Commented Mar 28 at 18:49

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The "Catalogue of Spacetimes" review of exact solutions to Einstein's equation, Mueller & Graves (2009), is the first place I would look. And sure enough section 2.22 might be what you are looking for. They pulled that metric from Perlick (2004), an LRR on gravitational lensing, which can point you further down the reference rabbit hole.

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  • $\begingroup$ Many thanks. I can guess that $a$ is the inverse of the angular speed, but cannot say what $\kappa$ stands for immediately...? $\endgroup$ Commented Mar 28 at 19:28

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