Randall-Sundrum Gauge in the Brane World

TL;DR

This paper analyzes the gauge choice in the Randall-Sundrum brane-world model, showing its restrictiveness for massless states, uniqueness for massive states, and its role in establishing the solution's stability.

Contribution

It clarifies the gauge conditions in the RS model and demonstrates the gauge's implications for stability and state descriptions.

Findings

$h_{55}=0$ and $h_{5ield$ are set to zero in the RS gauge.

The RS gauge is highly restrictive for massless states.

The RS gauge is unique for describing massive states.

Abstract

We discuss the Randall-Sundrum (RS) choice for $h_{MN}$ in the brane-world. We begin with the de Donder gauge (transverse-tracefree) including scalar($h_{55}$), vector($h_{5\mu}$) and tensor($h_{\mu\nu}$) in five dimensions for comparison. One finds that $h_{55}=0$ and $h_{5\mu}=0$. This leads to the RS choice. It appears that the RS choice is so restrictive for the five massless states, whereas it is unique for describing the massive states. Furthermore, one can establish the stability of the RS solution with the RS choice only.