Recovery of the Schwarzschild metric in theories with localized gravity beyond linear order - art. no. 024001

We solve the Einstein equations in the Randall-Sundrum framework with a sta tic, spherically symmetric matter distribution on the physical brane and ob tain an approximate expression for the gravitational field outside the sour ce to the second order in the gravitational coupling. This expression when confined on the physical brane coincides with the standard form of the Schw arzschild metric. Therefore, the Randall-Sundrum scenario is consistent wit h the Mercury precession and other tests of general relativity.