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It is argued that the braneworld gravity under the Schwarzschild ansatzshould obey three essential equations on the brane, and they are solvedexactly. We express the general solution of the fundamental equations of thebraneworld in power series of the brane normal coordinate. The power series arederived by solving three independent components of the bulk Einstein equation,and the coefficients are recursively determined in terms of five functions onthe brane. The other components of the bulk Einstein equation are automaticallysatisfied, as far as the five on-brane functions obey three essentialequations. They are the radial-extra and the extra-extra components of the bulkEinstein equation on the brane, and the equation of motion of the brane.Therefore the solution includes two arbitrary functions on the brane. We showthat the essential equations are exactly solved by choosing an appropriate setof the two arbitrary functions. The arbitrariness may affect the predictivepowers on the Newtonian and the post-Newtonian evidences.

Essential on-Brane Equations for the Braneworld Gravity under the Schwarzschild Ansatz