Discrete Spectrum of the Deficit Angle and the Differential Structure of a Cosmic String

TL;DR

This paper investigates the differential properties of scalar and electromagnetic fields around cosmic strings, revealing a discrete spectrum of deficit angles where fields remain smooth, linked to a quantization condition.

Contribution

It establishes a connection between the smoothness of fields at the cosmic string singularity and a discrete spectrum of deficit angles, introducing a quantization condition.

Findings

Fields are smooth inside the cosmic string space-time.

Smoothness breaks down at the singular boundary except for specific deficit angles.

A discrete spectrum of deficit angles is identified, related to a quantization condition.

Abstract

Differential properties of Klein-Gordon and electromagnetic fields on the space-time of a straight cosmic string are studied with the help of methods of the differential space theory. It is shown that these fields are smooth in the interior of the cosmic string space-time and that they loose this property at the singular boundary except for the cosmic string space-times with the following deficit angles : Delta=2\pi*(1-1/n), n=1,2,... A connection between smoothness of fields at the conical singularity and the scalar and electromagnetic conical bremsstrahlung is discussed. It is also argued that the smoothness assumption of fields at the singularity is equivalent to the Aliev and Gal'tsov "quantization" condition leading to the above mentioned discrete spectrum of the deficit angle.