  Wightman function, the vacuum expectation values of the field square and the
energy-momentum tensor are evaluated for a scalar field obeying mixed boundary
condition on a spherical brane in (D+1)-dimensional Rindler-like spacetime
$Ri\times S^{D-1}$, where $Ri$ is a two-dimensional Rindler spacetime. This
spacetime approximates the near horizon geometry of (D+1) -dimensional black
hole in the large mass limit. The vacuum expectation values are presented as
the sum of boundary-free and brane-induced parts. Further we extract from the
Wightman function for the boundary-free geometry the corresponding function in
the bulk $R^{2}\times S^{D-1}$. For the latter geometry the vacuum expectation
values of the field square and the energy-momentum tensor do not depend on the
spacetime point. For the renormalization of these quantities we use zeta
regularization technique. Various limiting cases of the brane-induced vacuum
expectation values are investigated.
