The Casimir force on a piston in Randall-Sundrum models

The Casimir effect of a piston for massless scalar fields which satisfy Dirichlet boundary conditions in the context of five-dimensional Randall-Sundrum models is studied. In these scenarios we derive and calculate the expression for the Casimir force on the piston. We also discuss the Casimir force in the limit that one outer plate is moved to the remote place to show that the nature of the reduced force between the parallel plates left. In the Randall-Sundrum model involving two branes the two plates attract each other when they locate very close, but the reduced Casimir force turns to be repulsive as the plates separation is not extremely tiny, which is against the experimental phenomena. In the case of one brane model the shape of the reduced Casimir force is similar to that of the standard two-parallel-system in the four-dimensional flat spacetimes while the sign of force remains negative.