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

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, we use the generalized Abel–Plana summation formula. As we shall see, this procedure allows us to extract from the vacuum expectation values the contribution coming from the unbounded spacetime and to explicitly present the boundary induced parts. As regards the boundary induced contribution, two distinct situations are examined: the vacuum average effects inside and outside the spherical shell. The asymptotic behaviour of the vacuum densities is investigated near the sphere centre and near the 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 the global monopole geometry, the sphere induced expectation values are exponentially suppressed. We discuss, as a special case, the fermionic vacuum densities for the spherical shell on the 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.