Randall–Sundrum choice in the brane world

We discuss the Randall–Sundrum (RS) choice for hMN in the brane world. We begin with the de Donder gauge (transverse-tracefree) including scalar(h55), vector(h5μ) and tensor(hμν) in five dimensions for comparison. One finds that h55=0 and h5μ=0. This leads to the RS choice. It appears that the RS choice is so restrictive for the five massless states, whereas it is unique for describing the massive states. Furthermore, one can establish the stability of the RS solution with the RS choice only.