Vacuum polarization induced by a cylindrical boundary in the cosmic string spacetime

TL;DR

This paper analyzes how a cylindrical boundary affects vacuum polarization phenomena for a scalar field in cosmic string spacetime, providing detailed formulas and asymptotic behaviors for various boundary conditions.

Contribution

It presents a comprehensive calculation of vacuum expectation values considering general Robin boundary conditions in cosmic string spacetime, including boundary effects and asymptotic analysis.

Findings

Boundary-induced vacuum polarization effects are explicitly calculated.

Asymptotic behaviors of vacuum expectation values are characterized in different limits.

Results are generalized to models with finite string core support.

Abstract

In this paper we investigate the Wightman function, the renormalized vacuum expectation values of the field square, and the energy-momentum tensor for a massive scalar field with general curvature coupling inside and outside of a cylindrical shell in the generalized spacetime of straight cosmic string. For the general case of Robin boundary condition, by using the generalized Abel-Plana formula, the vacuum expectation values are presented in the form of the sum of boundary-free and boundary-induced parts. The asymptotic behavior of the vacuum expectation values of the field square, energy density and stresses are investigated in various limiting cases. The generalization of the results to the exterior region is given for a general cylindrically symmetric static model of the string core with finite support.