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## Appendix A: Scalar Perturbations in the Generalized Longitudinal Gauge 

In this appendix we derive the linearized 5D Einstein and field equations for scalar per- turbations in the bulk. We linearize around a background metric of the form 

The background Einstein and field equations in these coordinates are 

<img src='content_image/340085.jpg'>

<img src='content_image/340086.jpg'>

<img src='content_image/340087.jpg'>

<img src='content_image/340084.jpg'>

