Electromagnetic vacuum densities induced by a cosmic string

TL;DR

This paper studies how a cosmic string affects electromagnetic vacuum properties in higher-dimensional spacetimes with flat and de Sitter geometries, revealing topological and gravitational influences on vacuum fluctuations.

Contribution

It provides explicit calculations of vacuum expectation values of electromagnetic fields and energy-momentum tensor in the presence of a cosmic string in various backgrounds, highlighting the effects of dimensionality and curvature.

Findings

Topological contributions can be positive or negative depending on parameters.

Vacuum densities are significantly altered by the background geometry.

Gravitational fields change the behavior of vacuum densities at large distances.

Abstract

We investigate the influence of a generalized cosmic string in (D+1) -dimensional spacetime on the local characteristics of the electromagnetic vacuum. Two special cases are considered with flat and locally de Sitter background geometries. The topological contributions in the vacuum expectation values (VEVs) of the squared electric and magnetic fields are explicitly separated. Depending on the number of spatial dimensions and on the planar angle deficit induced by the cosmic string, these contributions can be either negative or positive. In the case of the flat bulk, the VEV of the energy-momentum tensor is evaluated as well. For the locally de Sitter bulk, the influence of the background gravitational field essentially changes the behavior of the vacuum densities at distances from the string larger than the curvature radius of the spacetime.