No ghost state of Gauss-Bonnet interaction in warped backgrounds

A general solution to the Einstein field equations with Gauss-Bonnet(GB) term in the $AdS_5$ bulk background implies that the GB coupling $\alpha$ can take either sign (+ or -), though a positive $\alpha$ will be more meaningful. By considering linearized gravity with the GB term in the Randall-Sundrum(RS) a singular 3-brane model, we study the gravitational interactions between matter sources localized on the brane. With a correctly defined boundary condition on the brane, we find a smooth behavior of graviton propagator and hence the zero-mode solution as a 4d massless graviton localized on the brane with correct momentum and tensor structures. The coupling $\alpha$ modifies the graviton propagators both on the brane and in the bulk. The issue on ghost state of the GB term is resolved, and we find that there is no real ghost (negative norm) state of the GB term in the RS single brane picture. The latter condition leads to a consistency in the coupling between the brane matter and the bulk gravity. We also elucidate about the possibilities for behavior of a test particle on the brane and in the bulk.