Gravitating superconducting strings with timelike or spacelike currents

Betti Hartmann; Florent Michel

doi:10.1103/PhysRevD.86.105026

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Gravitating superconducting strings with timelike or spacelike currents

Betti Hartmann, Florent Michel

DOI 10.1103/PhysRevD.86.105026 · Physical Review D

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Abstract

We construct gravitating superconducting string solutions of the U(1)local×U(1)global model by solving the coupled system of Einstein and matter field equations numerically. We study the properties of these solutions in dependence on the symmetry breaking to Planck mass ratio. Using the macroscopic stability conditions formulated by Carter, we observe that the coupling to gravity allows for a new stable region that is not present in the flat space-time limit. We match the asymptotic metric to the Kasner metric and show that the relations between the Kasner coefficients and the energy per unit length and tension suggested previously are well fulfilled for symmetry breaking scale much smaller than the Planck mass. We also study the solutions to the geodesic equation in this space-time. While geodesics in the exterior space-time of standard cosmic strings are just straight lines, test particles experience a force in a general Kasner space-time, and as such, bound orbits are possible.