On linearized gravity in the Randall-Sundrum scenario

In the literature about the Randall-Sundrum scenario one finds on one hand that there exist (small) corrections to Newton’s law of gravity on the brane, and on another that the exact (and henceforth linearized) Einstein equations can be recovered on the brane. The explanation for these seemingly contradictory results is that the behaviour of the bulk far from the brane is different in both models. We show that explicitely in this paper.