Geodesics and Newton's Law in Brane Backgrounds

TL;DR

This paper investigates geodesic behavior and gravitational laws in brane world models, showing that particles are expelled from the brane in some models but that Newtonian gravity can still be recovered in alternative configurations.

Contribution

It analyzes geodesics in Randall-Sundrum models and proposes an alternative brane setup where gravity obeys Newton's law and particles remain on the brane.

Findings

Massive particles are expelled from the brane in the original model.

An alternative model with an attractive brane maintains Newtonian gravity.

Newton's law is valid on the brane in the alternative background.

Abstract

In brane world models our universe is considered as a brane imbedded into a higher dimensional space. We discuss the behaviour of geodesics in the Randall-Sundrum background and point out that free massive particles cannot move along the brane only. The brane is repulsive, and matter will be expelled from the brane into the extra dimension. This is rather undesirable, and hence we study an alternative model with a non-compact extra dimension, but with an attractive brane embedded into the higher dimensional space. We study the linearized gravity equations and show that Newton's gravitational law is valid on the brane also in the alternative background.