Abstract
We find exact solutions of the equations of motion for linearized gravity in the Randall–Sundrum model with matter on the branes and calculate the Newtonian limit of the model. The results established include the contributions of the radion and the massive gravitons, which essentially modify Newton's law at short distances. We consider the effects produced by “shadow” matter situated on the other brane and compare them with the effect of the usual matter for branes with positive and negative tension. We also calculate the deflection of light and Newton's law in the zero-mode approximation and explicitly isolate the contribution of the radion field.
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Volobuev, I.P., Smolyakov, M.N. Exact Solutions for Linearized Gravity in the Randall–Sundrum Model. Theoretical and Mathematical Physics 139, 458–472 (2004). https://doi.org/10.1023/B:TAMP.0000022739.83942.bc
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DOI: https://doi.org/10.1023/B:TAMP.0000022739.83942.bc