On linearized gravity in the Randall-Sundrum scenario

TL;DR

This paper clarifies the apparent contradictions in the Randall-Sundrum scenario regarding gravity corrections and Einstein equations by analyzing the behavior of the bulk spacetime.

Contribution

It provides a detailed analysis of the bulk behavior in the Randall-Sundrum model, reconciling previous conflicting results about gravity corrections and Einstein equations on the brane.

Findings

Bulk behavior differs significantly in the models.

Explicit calculations show how corrections to Newton's law arise.

Linearized Einstein equations are recovered on the brane.

Abstract

In the literature about the Randall-Sundrum scenario one finds on one hand that there exist (small) corrections to Newton's law of gravity on the brane, and on another that the exact (and henceforth linearized) Einstein equations can be recovered on the brane. The explanation for these seemingly contradictory results is that the behaviour of the bulk far from the brane is different in both models. We show that explicitely in this paper.