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We discuss gravitational perturbations in the Randall-Sundrum two branesmodel with radius stabilization. Following the idea by Goldberger and Wise forthe radius stabilization, we introduce a scalar field which has potentialslocalized on the branes in addition to a bulk potential. In our previous paperwe discussed gravitational perturbations induced by static, sphericallysymmetric and nonrelativistic matter distribution on the branes under thecondition that the values of the scalar field on the respective branes cannotfluctuate due to its extremely narrow brane potentials. We call this case thestrong coupling limit. Our concern in this paper is to generalize our previousanalysis relaxing the limitation of taking the strong coupling limit. We findthat new corrections in metric perturbations due to relaxing the strongcoupling limit enhance the deviation from the 4D Einstein gravity only in someexceptional cases. In the case that matter fields reside on the negativetension brane, the stabilized radion mass becomes very small when the newcorrection becomes large.Comment: 12 pages, No figures, typos correcte

Second order perturbations in the radius stabilized Randall-Sundrum two branes model. II. Effect of relaxing strong coupling approximation