Systematic study of the radion in the compact Randall-Sundrum model

We systematically study the question of identification and consistent inclusion of the radion, within the Lagrangian approach, in a two-brane Randall-Sundrum model. Exploiting the symmetry properties of the theory, we show how the radion can be identified unambiguously and give the action to all orders in the radion field and the metric. Using the background field method, we expand the theory to quadratic orders in the fields. We show that the most general classical solutions, for the induced metric on the branes in the case of a constant radion and a factorizable four-dimensional metric, correspond to Einstein spaces. We discuss extensively the diagonalization of the quadratic action. Furthermore, we obtain the four-dimensional effective theory from this and study the question of the spectrum as well as the couplings in these theories.