Simple fixed-brane gauges in $S_1/Z_2$ braneworlds

For five-dimensional braneworlds with an $S_1/\mathbb{Z}_2$ orbifold topology for the extra dimension $x^5$, we discuss the validity of recent claims that a gauge exists where the two boundary branes lie at fixed positions and the metric satisfies $g_{\mu 5}=\partial_5 g_{55}=0$ where $\mu$ labels the transverse dimensions. We focus on models where the bulk is empty apart from a negative cosmological constant, which, in the case of cosmological symmetry, implies the existence of a static frame with Schwarzschild-AdS geometry. Considering the background case with the branes moving apart after a collision, we show that such a gauge can be constructed perturbatively, expanding in either the time after collision or the brane velocity. Finally we examine how cosmological perturbations can be accommodated in such a gauge.