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With a view toward the problem of computing the linearized cosmologicalperturbations in Randall-Sundrum cosmological models where a Z2 symmetry hasbeen imposed about a boundary brane, we derive the form of the linearizedIsrael matching conditions and the auxiliary gauge conditions on the boundarywhen Lorentz gauge has been imposed in the bulk. This gauge is completelycovariant and local, manifestly respecting all the AdS5 symmetries in the bulkand not relying on a decomposition into pure scalar, vector, and tensorsectors, which is necessarily nonlocal. We demonstrate that the auxiliary gaugeconditions on the boundary ensure that bulk gravitons upon reflection off thebrane do not emit polarizations that violate the bulk Lorentz gauge condition.We also characterize the residual gauge freedom, embodied by five longitudinal(pure gauge) graviton polarizations in the bulk, four of which correspond toreparameterizations of the induced brane metric and one of which corresponds tonormal displacements of the brane.Comment: 35 pages, RevTeX, with two eps figure

Linearized Israel matching conditions for cosmological perturbations in a moving brane background