Initial condition of a thick loop cosmic string and linear perturbations

The initial data of the gravitational field produced by a loop thick string is considered. We show that the loop is not a geodesic on the initial hypersurface, while a loop conical singularity is. This suggests that there is the criteria in the string thickness at which the linear perturbation theory around flat space fails to describe the gravity produced by a loop cosmic string. Because the geodesics on the Euclid spacetime are not loops but straight lines. Using the above initial data, we show that the linear perturbation around flat Euclid space is plausible if the string thickness is larger than ∼ 5 × 10−3a, where a is the curvature radius of the string. PACS number(s): 04.20.Ex,04.40.-b,11.27.+d,98.80.Cq Typeset using REVTEX E-mail address : [email protected] 0