A Gauge-Invariant Unique Continuation Criterion for Waves in Asymptotically Anti-de Sitter Spacetimes

We reconsider the unique continuation property for a general class of tensorial Klein-Gordon equations form \begin{align*} \Box_{g} \phi + \sigma = \mathcal{G}(\phi,\nabla \phi) \text{,} \qquad \in \mathbb{R} \end{align*} on large asymptotically anti-de Sitter spacetimes. In particular, we aim to generalize previous results Holzegel, McGill, and second author [14,15,24] (which established above-mentioned through novel Carleman estimates near conformal boundary) in following ways: (1) replace so-called null convexity criterion (the key geometric assumption boundary needed [24] establish properties) by more that is also gauge invariant. (2) Our new can be applied from larger, domains boundary. (3) Similar [24], connect failure our generalized existence certain geodesics These used construct counterexamples continuation. Finally, gauge-invariant estimate will constitute ingredient proving full nonlinear Einstein-vacuum equations, which addressed forthcoming paper Holzegel [16].