Recovery of the Schwarzschild metric in theories with localized gravity beyond linear order

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Abstract
We solve the Einstein equations in the Randall-Sundrum framework with a static, spherically symmetric matter distribution on the physical brane and obtain an approximate expression for the gravitational field outside the source to the second order in the gravitational coupling. This expression when confined on the physical brane coincides with the standard form of the Schwarzschild metric. Therefore, the Randall-Sundrum scenario is consistent with the Mercury precession and other tests of general relativity.