Comment on `Wedges, cones, cosmic strings and their vacuum energy'

TL;DR

This paper extends previous work on vacuum energy around cosmic strings by analyzing the behavior of the quantum scalar stress tensor near conical singularities, revealing conditions for divergences based on geometric parameters.

Contribution

It provides a detailed analysis of the stress tensor near cones and wedges, identifying when divergences occur depending on the cone angle and geometric configurations.

Findings

Stress tensor components have singularities of order $r^ ext{gamma}$.

Divergences occur when the cone angle exceeds $2 extpi$.

Analytic solutions are possible for specific cone angles, avoiding divergences.

Abstract

A recent paper (2012 \emph{J. Phys.\ A} \textbf{45} 374018) is extended by investigating the behavior of the regularized quantum scalar stress tensor near the axes of cones and their covering manifold, the Dowker space. A cone is parametrized by its angle $\theta_1$, where $\theta_1=2\pi$ for flat space. We find that the tensor components have singularities of the type $r^\gamma$, but the generic leading $\gamma$ equals ${4\pi \over \theta_1} - 2$, which is negative if and only if $\theta_1>2\pi$, and is a positive integer if $\theta_1={2\pi\over N}$. Thus the functions are analytic in those cases that can be solved by the method of images starting from flat space, and they are not divergent in the cases that interpolate between those. As a wedge of angle $\alpha$ can be solved by images starting from a cone of angle $2\alpha$, a divergent stress can arise in a wedge with $\pi <\alpha \le 2\pi$ but not in a smaller one.