Gravitational Forces on the Branes

TL;DR

This paper investigates gravitational interactions in a 5D brane-world model, deriving how Newtonian gravity is recovered on the Planck brane and how forces behave on the TeV brane without stabilization mechanisms.

Contribution

It provides a linearized solution to Einstein's equations in a brane-world scenario, showing the behavior of gravitational forces on two branes with no brane bending effects.

Findings

Newton's law is recovered on the Planck brane.

Particles on the TeV brane experience exponentially growing attractive forces.

The model's Einstein equations are solved consistently without stabilization mechanisms.

Abstract

We examine the gravitational forces in a brane-world scenario felt by point particles on two 3-branes bounding a 5-dimensional AdS space with $S^{1}/Z_2$ symmetry. The particles are treated as perturbations on the vacuum metric and coordinate conditions are chosen so that no brane bending effects occur. We make an ADM type decomposition of the metric tensor and solve Einstein's equations to linear order in the static limit. While no stabilization mechanism is assumed, all the 5D Einstein equations are solved and are seen to have a consistent solution. We find that Newton's law is reproduced on the Planck brane at the origin while particles on the TeV brane a distance $y_2$ from the origin experience an attractive force that has a growing exponential dependence on the brane position.