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Stability and localization of the gravitational perturbations for a specialbrane system in Eddington-inspired Born-Infeld (EiBI) gravity were studied in[Phys. Rev. D 85, 124053 (2012)]. In this paper, we show that the gravitationalperturbations for a general brane system are stable, the four-dimensionalgraviton (massless KK graviton) can be localized on the brane, and the massspectrum of massive KK gravitons are gapless and continuous. Two models areconstructed as examples. In the first model, which is a generalization of[Phys. Rev. D 85, 124053 (2012)], the brane has no inner structure and there isno gravitational resonance (quasi-localized KK gravitons). In the second one,the background scalar field is a double-kink when the parameter in the modelapproaches its critical value. Correspondingly, the brane has inner structureand some gravitational resonances appear.

Stability and (quasi-)localization of gravitational fluctuations in Eddington-Inspired Born-Infeld brane system