Lagrangian formalism of gravity in the Randall-Sundrum model

We derive the effective Lagrangian of the physical four-dimensional fields in the Randall-Sundrum (RS) model, and use this to calculate the Newtonian gravitational potential between two point sources on the brane. The effect of the radion is emphasized, and it is shown to disappear when the hidden brane is taken to infinity, i.e. when we only have one brane. As a preliminary, we derive the corresponding Lagrangian in the simpler geometry of a flat spacetime with one extra dimension compactified on a torus. We also study the gauge invariance of the theory, and note that the massless vector field that is present for the torus disappears in the RS model because of the orbifold symmetry.