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Casimir densities for two spherical branes in Rindler-like spacetimes

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.