Vacuum Polarization of a Massless Scalar Field in the Background of a Global Monopole with Finite Core

TL;DR

This paper investigates how the finite core structure of a global monopole influences vacuum polarization effects of a massless scalar field, revealing significant contributions for specific coupling values.

Contribution

It introduces a detailed analysis of vacuum polarization in a global monopole with finite core, including calculations of the Green function and corrections to vacuum expectation values.

Findings

Inner structure significantly affects vacuum polarization for certain couplings.

Corrections to the energy-momentum tensor depend on the monopole's core structure.

The Euclidean Green function is explicitly calculated for the system.

Abstract

In this paper we analyze the vacuum polarization effects of a massless scalar field in the background of a global monopole considering a inner structure to it. Specifically we investigate the effect of its structure on the vacuum expectation value of the square of the field operator, $<\hat{\Phi}^2(x)>$, admitting a non-minimal coupling between the field with the geometry: $\xi {\cal{R}}\hat{\Phi}^2$. Also we calculate the corrections on the vacuum expectation value of the energy-momentum tensor, $<\hat{T}_{\mu\nu}>$, due to the inner structure of the monopole. In order to develop these analysis, we calculate the Euclidean Green function associated with the system for points in the region outside the core. As we shall see, for specific value of the coupling parameter $\xi$, the corrections caused by the inner structure of the monopole can provide relevant contributions on these vacuum polarizations.