Spinor Casimir densities for a spherical shell in the global monopole spacetime

TL;DR

This paper calculates the vacuum energy densities of a spinor field around a spherical shell in a global monopole spacetime, revealing how boundary conditions and spacetime curvature influence quantum vacuum effects.

Contribution

It provides a detailed analysis of fermionic vacuum densities in a global monopole background with spherical boundary conditions, extending previous models to a local quantum field theory context.

Findings

Boundary-induced vacuum densities are suppressed in strong gravitational fields.

Explicit expressions for vacuum expectation values inside and outside the shell.

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

Abstract

We investigate the vacuum expectation values of the energy-momentum tensor and the fermionic condensate associated with a massive spinor field obeying the MIT bag boundary condition on a spherical shell in the global monopole spacetime. In order to do that it was used the generalized Abel-Plana summation formula. As we shall see, this procedure allows to extract from the vacuum expectation values the contribution coming from to the unbounded spacetime and explicitly to present the boundary induced parts. As to the boundary induced contribution, two distinct situations are examined: the vacuum average effect inside and outside the spherical shell. The asymptotic behavior of the vacuum densities is investigated near the sphere center and surface, and at large distances from the sphere. In the limit of strong gravitational field corresponding to small values of the parameter describing the solid angle deficit in global monopole geometry, the sphere-induced expectation values are exponentially suppressed. As a special case we discuss the fermionic vacuum densities for the spherical shell on background of the Minkowski spacetime. Previous approaches to this problem within the framework of the QCD bag models have been global and our calculation is a local extension of these contributions.