The Geometry of Massless Cosmic Strings

TL;DR

This paper explores the geometry of massless cosmic strings, revealing that they create a flat spacetime with a conical singularity characterized by a null-rotation holonomy, and provides a smooth metric description.

Contribution

It introduces a detailed geometric description of massless cosmic strings using holonomy and constructs a smooth metric outside the singularity.

Findings

Massless cosmic strings produce a flat spacetime with a conical singularity.

The holonomy of such strings is a null-rotation Lorentz transformation.

No gravitational shockwave is associated with massless cosmic strings.

Abstract

We study the geometry generated by a massless cosmic string. We find that this is given by a Riemann flat spacetime with a conical singularity along the worldsheet of the string. The geometry of such a spacetime is completely fixed by the holonomy of a simple loop wrapping the conical singularity. In the case of a massless cosmic string, this holonomy is a null-rotation/parabolic Lorentz transformation with a parabolic angle given by the linear energy density of the cosmic string. This description explicitly shows that there is no gravitational shockwave accompanying the massless cosmic string as has been suggested in the past. To illustrate the non-singular nature of the surrounding geometry, we construct a metric for the massless cosmic string that is smooth everywhere outside the conical singularity.