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We evaluate the Casimir energy and force for a massive scalar field withgeneral curvature coupling parameter, subject to Robin boundary conditions ontwo codimension-one parallel plates, located on a $(D+1)$-dimensionalbackground spacetime with an arbitrary internal space. The most general case ofdifferent Robin coefficients on the two separate plates is considered. Withindependence of the geometry of the internal space, the Casimir forces are seento be attractive for special cases of Dirichlet or Neumann boundary conditionson both plates and repulsive for Dirichlet boundary conditions on one plate andNeumann boundary conditions on the other. For Robin boundary conditions, theCasimir forces can be either attractive or repulsive, depending on the Robincoefficients and the separation between the plates, what is actually remarkableand useful. Indeed, we demonstrate the existence of an equilibrium point forthe interplate distance, which is stabilized due to the Casimir force, and showthat stability is enhanced by the presence of the extra dimensions.Applications of these properties in braneworld models are discussed. Finally,the corresponding results are generalized to the geometry of a piston ofarbitrary cross section.

Repulsive Casimir effect from extra dimensions and Robin boundary conditions: from branes to pistons