Comment on "Metric Fluctuations in Brane Worlds"

TL;DR

This paper refutes a recent claim that certain metric perturbations in brane world models are non-localized and unstable, demonstrating that the problematic dependence on the extra dimension can be gauged away, preserving the stability argument.

Contribution

It clarifies that the linear dependence on the extra dimension in the perturbation is a gauge artifact, reaffirming the localization of gravity in Randall and Sundrum's model.

Findings

Linear dependence on the extra dimension can be gauged away.

The physical perturbation does not depend on the extra coordinate.

Randall and Sundrum's localization argument remains valid.

Abstract

Recently, Ivanov and Volovich (hep-th/9912242) claimed that the perturbation of $h_{\mu\nu}$ with nonvanishing transverse components $h_{5\mu}$ is not localized on the brane because $h_{\mu\nu}$ depends on the fifth coordinate $z$ linearly. Consequently, it may indicate that the effective theory is unstable. However, we point out that such linear dependence on $z$ can be {\it gauged away}. Hence the solution does not belong to the physical one. Therefore, even if one includes $h_{5\mu}$, Randall and Sundrum's argument for the localized gravity on the brane remains correct.