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

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.

Wightman function and scalar Casimir densities for a wedge with two cylindrical boundaries

“…By taking the coincidence limit, we have obtained similar representations for the VEVs of the field square and the energy-momentum tensor, formulae (25) and (34). More symmetric decompositions are given by formulae (31) and (42), where the last interference term is finite everywhere including points on the shells. In the limit a → 0 the interference parts tends to zero like a 2q .…”

“…The corresponding Casimir densities for the electromagnetic field with perfect conductor boundary conditions on bounding surfaces are considered in [30]. The closely related problem with a cylindrical shell in the geometry of a cosmic string is discussed in [31,32] for scalar and electromagnetic fields. In both scalar and electromagnetic cases the application of a variant of the generalized Abel-Plana formula [24] enables to extract from the vacuum expectation values the parts corresponding to the geometry of a wedge without the cylindrical shell and to present the shell induced parts in terms of rapidly converging integrals.…”

Vacuum polarization by a global monopole with finite core

“…The influence of the non-trivial core structure for the cosmic string on a quantum scalar field has been considered in Refs. [21,22,23]. In the discussion below we will assume that n > 0.…”

“…The corresponding model for the cosmic string core was considered in Refs. [21,22,23] and following these papers we will refer to this model as flower-pot model. Taking u(r) = v(r) = 0 from the zero curvature condition one finds e w(r) = r + const.…”

Electromagnetic Casimir densities induced by a conducting cylindrical shell in the cosmic string spacetime

“…This is the well-known Casimir effect (for a review see [27]). In a previous paper [28], we have studied the configuration with both types of sources for the polarization of the scalar vacuum, namely, a cylindrical boundary and a cosmic string, assuming that the boundary is coaxial with the string and that on this surface the scalar field obeys Robin boundary condition. For a massive scalar field with an arbitrary curvature coupling parameter we evaluated the Wightman function and the vacuum expectation values of the field square and the energy-momentum tensor.…”