Casimir densities for a spherical shell in the global monopole background

TL;DR

This paper analyzes the vacuum expectation values of the energy-momentum tensor for a scalar field in a global monopole background with a spherical boundary, deriving explicit formulas and studying asymptotic behaviors.

Contribution

It provides new explicit formulas for vacuum densities in a global monopole background with a spherical boundary, including regularization and asymptotic analysis.

Findings

Boundary induced vacuum stresses are strongly anisotropic for small solid angle deficits.

Explicit integral expressions for vacuum expectation values are derived, facilitating numerical analysis.

Asymptotic behaviors near the sphere surface and at large distances are characterized.

Abstract

We investigate the vacuum expectation values for the energy-momentum tensor of a massive scalar field with general curvature coupling and obeying the Robin boundary condition on a spherical shell in the $D+1$-dimensional global monopole background. The expressions are derived for the Wightman function, the vacuum expectation values of the field square, the vacuum energy density, radial and azimuthal stress components in both regions inside and outside the shell. A regularization procedure is carried out by making use of the generalized Abel-Plana formula for the series over zeros of cylinder functions. This formula allows us to extract from the vacuum expectation values the parts due to the global monopole gravitational field in the situation without a boundary, and to present the boundary induced parts in terms of exponentially convergent integrals, useful, in particular, for numerical calculations. The asymptotic behavior of the vacuum densities is investigated near the sphere surface and at large distances. We show that for small values of the parameter describing the solid angle deficit in global monopole geometry the boundary induced vacuum stresses are strongly anisotropic.