The radion and the perturbative metric in RS1

TL;DR

This paper derives and simplifies the linearized metric perturbations in the Randall-Sundrum 1 model, showing their equivalence to previous solutions through gauge transformations.

Contribution

It provides a clear, decoupled form of the perturbative Einstein equations and demonstrates the equivalence of different metric ansatzes via gauge transformations.

Findings

Derived a simple, decoupled perturbative metric ansatz.

Showed equivalence of different metric ansatzes through gauge transformations.

Connected the perturbative solution to previous exact solutions.

Abstract

We calculate the linearized metric perturbations in the five dimensional two-brane model of Randall and Sundrum. In a carefully chosen gauge, we write down and decouple Einstein equations for the perturbations and get the final and simple perturbative metric ansatz. This ansatz turns out to be equal to the linear expansion of the metric solution of Charmousis et al. \cite{rubakov}. We show that this ansatz, the metric ansatz of Boos et al. \cite{boos} and the one of Das and Mitov \cite{das} are not incompatible, as it appears on the surface, but completely equivalent by an allowed gauge transformation that we give.