  We evaluate the Casimir energy and force for a massive scalar field with
general curvature coupling parameter, subject to Robin boundary conditions on
two codimension-one parallel plates, located on a $(D+1)$-dimensional
background spacetime with an arbitrary internal space. The most general case of
different Robin coefficients on the two separate plates is considered. With
independence of the geometry of the internal space, the Casimir forces are seen
to be attractive for special cases of Dirichlet or Neumann boundary conditions
on both plates and repulsive for Dirichlet boundary conditions on one plate and
Neumann boundary conditions on the other. For Robin boundary conditions, the
Casimir forces can be either attractive or repulsive, depending on the Robin
coefficients and the separation between the plates, what is actually remarkable
and useful. Indeed, we demonstrate the existence of an equilibrium point for
the interplate distance, which is stabilized due to the Casimir force, and show
that 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 of
arbitrary cross section.

High Energy Physics - Theory;General Relativity and Quantum Cosmology;Quantum Physics