Abstract
A treatment of linearized gravity with the Einstein-Gauss-Bonnet interaction terms in $D\geq$ 5 is given in the Randall-Sundrum brane background. This Letter has outlined some interesting features of the brane world gravity and Newtonian potential correction with the GB interaction term. We find that the GB coupling $\alpha$ renormalizes the effective four-dimensional Newton constant on the brane, and also additionally contributes to the correction term of the Newtonian potential. Indeed, the GB term does not affect the massless graviton mode and the Einstein gravity on the brane, and quite interestingly, such term in $D\geq 5$ appears to give more information about the necessary boundary condition(s) to be satisfied by the zero mode wavefunction on the brane(s). small (and preferably positive) GB coupling $\alpha$.
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