Vacuum fluctuations and boundary conditions in a global monopole

We study the vacuum fluctuations of a massless scalar field (psi) over cap on the background of a global monopole. Due to the nontrivial topology of the global monopole spacetime characterized by a solid deficit angle, parametrized by eta(2), we expect that <(psi) over cap (2)>(ren) and <(T) over cap (mu nu)>(ren) are nonzero and proportional to eta(2), so that they annul in the Minkowski limit eta -> 0. However, due to the naked singularity at the monopole core, the evolution of the scalar field is not unique. In fact, they are in one-to-one correspondence with the boundary conditions which turn into self-adjoint the spatial part of the wave operator. We show that only the Dirichlet boundary condition corresponds to our expectations and gives zero contribution to the vacuum fluctuations in the Minkowski limit. All other boundary conditions give nonzero contributions in this limit due to the nontrivial interaction between the field and the singularity.