Weak-Field Gravity of Revolving Circular Cosmic Strings

TL;DR

This paper derives a weak-field Einstein's solution for a revolving circular cosmic string, revealing that its conical deficit angle remains unchanged by its angular velocity, similar to a straight string.

Contribution

It presents the first weak-field solution for a revolving circular cosmic string, showing the deficit angle is unaffected by the string's angular velocity.

Findings

Deficit angle equals that of a straight string with same energy density

Revolving motion does not alter the conical singularity

Solution demonstrates stability of the deficit angle under revolution

Abstract

A weak-field solution of Einstein's equations is constructed. It is generated by a circular cosmic string revolving in its plane about the centre of the circle. (The revolution is introduced to prevent the string from collapsing.) This solution exhibits a conical singularity, and the corresponding deficit angle is the same as for a straight string of the same linear energy density, irrespective of the angular velocity of the string.