Tensor perturbations of f(R)-branes

We analyze the tensor perturbations of flat thick domain wall branes in f(R) gravity. Our results indicate that under the transverse and traceless gauge, the metric perturbations decouple from the perturbation of the scalar field. Besides, the perturbed equation reduces to the familiar Klein-Gordon equation for massless spin-2 particles only when the bulk curvature is a constant or when f(R)=R. As an application of our results, we consider the possibility of localizing gravity on some flat thick branes. The stability of these brane solutions is also shortly discussed.