  The nonlinear gravitational interaction is investigated in the
Randall-Sundrum two branes model with the radius stabilization mechanism. As
the stabilization model, we assume a single scalar field that has a potential
in the bulk and a potential on each brane. We develop a formulation of the
second order gravitational perturbations under the assumption of a static and
axial-symmetric five-dimensional metric that is spherically symmetric in the
four-dimensional sense. After deriving the formal solutions for the
perturbations, we discuss the gravity on each brane induced by the matter on
its own side, taking the limit of large coupling of the scalar field
interaction term on the branes. We show using the Goldberger-Wise stabilization
model that four-dimensional Einstein gravity is approximately recovered in the
second order perturbations.
