Weak-Field Gravity of Circular Cosmic Strings

TL;DR

This paper derives a weak-field Einstein's solution for a circular cosmic string, confirming the deficit angle matches that of a straight string, supporting previous theoretical assumptions about string loops.

Contribution

It provides the first weak-field metric solution for a circular cosmic string, validating the deficit-angle assumption for string loops at symmetry.

Findings

The solution exhibits a conical singularity.

The deficit angle equals that of a straight string with same energy density.

Supports the Frolov-Israel-Unruh derivation of string loop metrics.

Abstract

A weak-field solution of Einstein's equations is constructed. It is generated by a circular cosmic string externally supported against collapse. The solution exhibits a conical singularity, and the corresponding deficit angle is the same as for a straight string of the same linear energy density. This confirms the deficit-angle assumption made in the Frolov-Israel-Unruh derivation of the metric describing a string loop at a moment of time symmetry.