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We obtain an effective theory for the radion dynamics of the two-braneRandall Sundrum model, correct to all orders in brane velocity in the limit ofclose separation, which is of interest for studying brane collisions and earlyUniverse cosmology. Obtained via a recursive solution of the Bulk equation ofmotions, the resulting theory represents a simple extension of thecorresponding low-energy effective theory to the high energy regime. Thefour-dimensional low-energy theory is indeed not valid when corrections atsecond order in velocity are considered. This extension has the remarkableproperty of including only second derivatives and powers of first orderderivatives. This important feature makes the theory particularly easy tosolve. We then extend the theory by introducing a potential and detuning thebranes.Comment: Version published in the Physical Review

High-energy theory for close Randall-Sundrum branes