Vacuum polarization by a flat boundary in cosmic string spacetime

TL;DR

This paper investigates how a flat boundary affects vacuum polarization in higher-dimensional cosmic string spacetimes, revealing that the cosmic string's topology amplifies boundary-induced effects and induces normal stresses.

Contribution

It provides explicit expressions for vacuum expectation values considering boundary effects in cosmic string spacetime, extending previous boundary-free analyses.

Findings

Boundary enhances vacuum polarization effects compared to Minkowski space.

Cosmic string topology induces non-zero normal stress on the boundary.

Vacuum forces on the boundary are quantitatively analyzed.

Abstract

In this paper we analyze the vacuum expectation values of the field squared and the energy-momentum tensor associated to a massive scalar field in a higher dimensional cosmic string spacetime, obeying Dirichlet or Neumann boundary conditions on the surface orthogonal to the string. In order to develop this analysis the corresponding Green function is obtained. The Green function is given by the sum of two expressions: the first one corresponds to the standard Green function in the boundary-free cosmic string spacetime and the second contribution is induced by the boundary. The boundary induced parts have opposite signs for Dirichlet and Neumann scalars. Because the analysis of vacuum polarization effects in the boundary-free cosmic string spacetime have been developed in the literature, here we are mainly interested in the calculations of the effects induced by the boundary. In this way closed expressions for the corresponding expectation values are provided, as well as their asymptotic behavior in different limiting regions is investigated. We show that the non-trivial topology due to the cosmic string enhances the boundary induced vacuum polarization effects for both field squared and the energy-momentum tensor, compared to the case of a boundary in Minkowski spacetime. The presence of the cosmic string induces non-zero stress along the direction normal to the boundary. The corresponding vacuum force acting on the boundary is investigated.