We discuss the role of the trace part of metric fluctuations $h_{ MN}$ in the Randall-Sundrum scenario of gravity. Without the matter, this field ($h=\eta^{ MN}h_{ MN}$) is a gauge-dependent term, and thus it can be gauged away. But, including the uniform source $\tilde{ T}_{ MN}$, this field satisfies the linearized equation $\Box_4 h =16\pi G_5 T^{ \mu}_{ \mu}$. This may correspond to the scalar $\xi^5$ in the bending of the brane due to the localized source. Considering the case of longitudinal perturbations ($h_{ 5\mu} =h_{ 55}=0$), one finds the source relation $\tilde{ T}^{ \mu}_{ \mu}=2\tilde{ T}_{ 55}$, which leads to the ghost states in the massive modes. In addition, if one requires $T_{ 44}=2(T_{ 22}+T_{ 33})$, it is found that in the limit of $m^2_h \to 0$ 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.
Categories: hep-th gr-qc