Initial condition of a thick loop cosmic string and linear perturbations

Abstract

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 ``{\it 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 $\sim 5\times 10^{-3}a$, where $a$ is the curvature radius of the loop.

21 pages, 4 figures, RevTeX. Some spelling / grammar typos are corrected. Accepted for publication in Classical and Quantum Gravity

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Cited by in corpus (2)

• Perturbations of Matter Fields in the Second-order Gauge-invariant Cosmological Perturbation Theory
• Construction of gauge-invariant variables of linear metric perturbations on an arbitrary background spacetime