Vacuum polarization by a flat boundary in cosmic string spacetime

In this paper, we analyze the vacuum expectation values of the field squared and the energy-momentum tensor associated with a massive scalar field in a higher dimensional cosmic string spacetime, obeying Dirichlet or Neumann boundary conditions on the surface orthogonal to the string. In order to develop this analysis, the corresponding Green's function is obtained. The Green's function is given by the sum of two expressions: the first one corresponds to the standard Green's function in the boundary-free cosmic string spacetime and the second contribution is induced by the boundary. The boundary-induced parts have opposite signs for Dirichlet and Neumann scalars. Because the analysis of vacuum polarization effects in the boundary-free cosmic string spacetime has been developed in the literature, here we are mainly interested in the calculations of the effects induced by the boundary. In this way closed expressions for the corresponding expectation values are provided, as well as their asymptotic behavior in different limiting regions being investigated. We show that the non-trivial topology due to the cosmic string enhances the boundary-induced vacuum polarization effects for both the field squared and the energy-momentum tensor, compared to the case of a boundary in Minkowski spacetime. The presence of the cosmic string induces non-zero stress along the direction normal to the boundary. The corresponding vacuum force acting on the boundary is investigated.