No ghost state in the brane world

We discuss the role of the trace part of metric fluctuations hMN in the Randall–Sundrum scenario of gravity. Without the matter, this field (h=ηMNhMN) is a gauge-dependent term, and thus it can be gauged away. But, including the uniform source T̃MN, this field satisfies the linearized equation □4h=16πG5Tμμ. This may correspond to the scalar ξ5 in the bending of the brane due to the localized source. Considering the case of longitudinal perturbations (h5μ=h55=0), one finds the source relation T̃μμ=2T̃55, which leads to the ghost states in the massive modes. In addition, if one requires T44=2(T22+T33), it is found that in the limit of m2h→0 we have the massless spin-2 propagation without the ghost state. This exactly corresponds to the same situation as in the intermediate scales of Gregory–Rubakov–Sibiryakov (GRS) model.