Evaluation of vacuum energy density around geometrical defects by the WKB method

TL;DR

This paper uses the WKB method to estimate the vacuum energy density around cosmic strings and monopoles, showing it aligns well with exact methods and providing a practical approximation technique.

Contribution

It demonstrates the effectiveness of the WKB approximation in calculating vacuum energy densities around geometrical defects, matching known exact results.

Findings

WKB method reproduces exact energy densities around cosmic strings.

The approximation agrees well with exact results in three-dimensional cases.

The method is successfully applied to global monopoles.

Abstract

The energy density of a conformally invariant scalar field around a cosmic string is estimated by the WKB method. This approach reproduces the precise value obtained by the other authors using the exact mode-sum method or the method of mirror images. The approximation is also in good agreement with the exact result in the three-dimensional case. We also evaluate the energy density of a conformally invariant scalar field around a global monopole by the same way and find the known result again.