ar X iv : h ep - t h / 04 12 01 6 v 3 1 7 Ju n 20 05 Gravitational Forces in the Brane World

We consider the problem of gravitational forces between point particles on the branes in a Randall-Sundrum (R-S) two brane model with S 1 /Z 2 symmetry. Matter is assumed to produce a perturbation to the R-S vacuum metric and all the 5D Einstein equations are solved to linearized order (for arbitrary matter on both branes). We show that while the gauge condition h i5 = 0, i = 0, 1, 2, 3 can always be achieved without brane bending, the condition h 55 = 0 leads to large brane bending. The static potential arising from the zero modes and the corrections due to the Kaluza-Klein (KK) modes are calculated. Gravitational forces on the Planck (y 1 = 0) brane recover Newtonian physics with small KK corrections (in accord with other work). However , forces on the TeV (y 2) brane due to particles on that brane are strongly distorted by large R-S exponentials.