Instability of the Randall-Sundrum Model and Exact Bulk Solutions

TL;DR

This paper investigates the stability of the Randall-Sundrum two-brane model by analyzing gravitational forces in the bulk, proposing a fluid-filled bulk model, and deriving exact solutions that embed 4D Einstein solutions, with implications for extra dimension compactification.

Contribution

It introduces a fluid bulk model with anisotropic pressure and derives exact solutions, showing how 4D Einstein solutions can be embedded in the bulk for equilibrium.

Findings

Bulk gravitational force can destabilize the model.

A fluid with anisotropic pressure can stabilize the bulk.

Exact solutions demonstrate embedding of 4D Einstein solutions.

Abstract

Five dimensional geodesic equation is used to study the gravitational force acted on a test particle in the bulk of the Randall-Sundrum two-brane model.This force could be interpreted as the gravitational attraction from matters on the two branes and may cause the model to be unstable. By analogy with star models in astrophysics, a fluid RS model is proposed in which the bulk is filled with a fluid and this fluid has an anisotropic pressure to balance the gravity from the two branes. Thus a class of exact bulk solutions is obtained which shows that any 4D Einstein solution with a perfect fluid source can be embedded in $y=$ constant hypersurfaces in the bulk to form an equilibrium state of the brane model. By requiring a 4D effective curvature to have a minimum, the compactification size of the extra dimension is discussed.