  Wightman function, the vacuum expectation values of the field square and the
energy-momentum tensor are evaluated for a scalar field obeying the Robin
boundary conditions on two spherical branes in (D+1)-dimensional Rindler-like
spacetime $Ri\times S^{D-1}$, with a two-dimensional Rindler spacetime $Ri$.
This spacetime approximates the near horizon geometry of (D+1)-dimensional
black hole. By using the generalized Abel-Plana formula, the vacuum expectation
values are presented as the sum of single brane and second brane induced parts.
Various limiting cases are studied. The vacuum forces acting on the branes are
decomposed into the self-action and interaction terms. The interaction forces
are investigated as functions of the brane locations and coefficients in the
boundary conditions.
