  We generalize our unique continuation results recently established for a
class of linear and nonlinear wave equations $\Box_g \phi + \sigma \phi =
\mathcal{G} ( \phi, \partial \phi )$ on asymptotically anti-de Sitter (aAdS)
spacetimes to aAdS spacetimes admitting non-static boundary metrics. The new
Carleman estimates established in this setting constitute an essential
ingredient in proving unique continuation results for the full nonlinear
Einstein equations, which will be addressed in forthcoming papers. Key to the
proof is a new geometrically adapted construction of foliations of pseudoconvex
hypersurfaces near the conformal boundary.
