Gravitational Forces in the Brane World

TL;DR

This paper analyzes gravitational interactions in a two-brane Randall-Sundrum model, deriving the linearized metric perturbations and showing how gravity behaves differently on the two branes, with Newtonian limits on the Planck brane and distortions on the TeV brane.

Contribution

It provides a detailed calculation of gravitational forces including Kaluza-Klein corrections in the Randall-Sundrum two-brane setup, highlighting the effects of brane bending and mode contributions.

Findings

Newtonian gravity is recovered on the Planck brane with small KK corrections.

Gravitational forces on the TeV brane are significantly distorted by exponential factors.

Large brane bending occurs when imposing the gauge condition $h_{55} = 0$.

Abstract

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.