The four-dimensional effective action of a multibrane world in five dimensions

We present an analysis of the gravitational behaviour of an $N$-brane model in five dimensions under general conditions. A two-lengthscale expansion is used to obtain a low-energy description of the model, allowing us to compute a four-dimensional effective theory in this regime. We find $N-1$ radion modes in a non-linear sigma model with the target space being hyperbolic space. Our analysis produces exact solutions of the five-dimensional equations of motion, although the stability of these solutions is known to break down in the case of a black hole on a brane.