ИСТИНА

We analyze the gravity-induced effects associated with a massless scalar field in a higher-dimensional spacetime being the tensor product of $(d-n)$-dimensional Minkowski space and $n$-dimensional spherically-symmetric space with angle deficit. These spacetimes are considered as simple models for a multidimensional global monopole or cosmic string. In terms of the angular deficit value, we derive the perturbative expression for the scalar Green's function and compute it to the leading order. With the use of this Green's function we compute the renormalized vacuum expectation value of the field square and the renormalized vacuum averaged of the scalar-field's energy-momentum tensor for arbitrary $d$ and $n$ and arbitrary coupling constant to the curvature $\xi$.