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The nonlinear gravitational interaction is investigated in theRandall-Sundrum two branes model with the radius stabilization mechanism. Asthe stabilization model, we assume a single scalar field that has a potentialin the bulk and a potential on each brane. We develop a formulation of thesecond order gravitational perturbations under the assumption of a static andaxial-symmetric five-dimensional metric that is spherically symmetric in thefour-dimensional sense. After deriving the formal solutions for theperturbations, we discuss the gravity on each brane induced by the matter onits own side, taking the limit of large coupling of the scalar fieldinteraction term on the branes. We show using the Goldberger-Wise stabilizationmodel that four-dimensional Einstein gravity is approximately recovered in thesecond order perturbations.Comment: 23 pages, no figures, typos correcte

Second order perturbations in the radius stabilized Randall-Sundrum two branes model