Vacuum polarization by a global monopole with finite core

We investigate the effects of a $(D+1)$-dimensional global monopole core on the behavior of a quantum massive scalar field with general curvature coupling parameter. In the general case of the spherically symmetric static core, formulae are derived for the Wightman function, for the vacuum expectation values of the field square and the energy-momentum tensor in the exterior region. These expectation values are presented as the sum of point-like global monopole part and the core induced one. The asymptotic behavior of the core induced vacuum densities is investigated at large distances from the core, near the core and for small values of the solid angle corresponding to strong gravitational fields. In particular, in the latter case we show that the behavior of the vacuum densities is drastically different for minimally and non-minimally coupled fields. As an application of general results the flower-pot model for the monopole's core is considered and the expectation values inside the core are evaluated.