Abstract
The stability and localization of the gravitational perturbations for a special brane system in Eddington-inspired Born-Infeld gravity were studied in Liu et al. [Phys. Rev. D 85, 124053 (2012)]. In this paper, we show that the gravitational perturbations for a general brane system are stable, the four-dimensional graviton (massless KK graviton) can be localized on the brane, and the mass spectra of massive KK gravitons are gapless and continuous. Two models are constructed as examples. In the first model, which is a generalization of Liu et al. [Phys. Rev. D 85, 124053 (2012)], the brane has no inner structure and there is no gravitational resonance (quasilocalized KK gravitons). In the second one, the background scalar field is a double kink when the parameter in the model approaches its critical value. Correspondingly, the brane has inner structure and some gravitational resonances appear.
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