Initial condition of a gravitating 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 a thick loop is not a geodesic on the initial hypersurface, while a loop conical singularity is. This suggests that there is the “critical thickness” of a string, at which the linear perturbation theory with a flat space background fails to describe the gravity of a loop cosmic string. Using the above initial data, we also show that the linear perturbation around flat space is plausible if the string thickness is larger than ∼ 5×10−3a, where a is the curvature radius of the loop. PACS number(s): 04.20.Ex,04.40.-b,11.27.+d,98.80.Cq Typeset using REVTEX E-mail address : [email protected] 0