Induced vacuum magnetic field in the cosmic string background

TL;DR

This paper investigates how a cosmic string's presence induces a magnetic field in the vacuum, deriving explicit expressions for the induced field and analyzing the effects of boundary conditions and symmetries.

Contribution

It provides a detailed analysis of vacuum-induced magnetic fields around cosmic strings, including boundary condition effects and symmetry considerations, with explicit formulas for the induced fields.

Findings

A magnetic flux tube encloses the cosmic string.

The induced magnetic field depends on string flux, tension, and size.

Boundary conditions are constrained by physical plausibility.

Abstract

The relativistic charged spinor matter field is quantized in the background of a straight cosmic string with nonvanishing transverse size. The most general boundary conditions ensuring the impossibility for matter to penetrate through the edge of the string core are considered. The role of discrete symmetries is elucidated, and analytic expressions for the temporal and spatial components of the induced vacuum current are derived in the case of either $P$ or $CT$ invariant boundary condition with two parameters varying arbitrarily from point to point of the edge. The requirement of physical plausibility for the global induced vacuum characteristics is shown to remove completely an arbitrariness in boundary conditions. We find out that a magnetic field is induced in the vacuum and that a sheath in the form of a tube of the magnetic flux lines encloses a cosmic string. The dependence of the induced vacuum magnetic field strength on the string flux and tension, as well as on the transverse size of the string and on the distance from the string, is unambiguously determined.