In theoretical physics, it is often conjectured that a correspondence exists between the gravitational dynamics of asymptotically Anti-de Sitter (AdS) spacetimes and a conformal field theory of their boundaries. In the context of classical relativity, one can attempt to rigorously formulate such a correspondence statement as a unique continuation problem for PDEs: Is an asymptotically AdS solution of the Einstein equations uniquely determined by its data on its conformal boundary at infinity?

In this presentation, we present a key step toward this problem: we establish unique continuation results for wave equations on fixed asymptotically AdS spacetimes. We will also discuss applications of these results toward symmetry extension and rigidity theorems. One example is toward determining when a symmetry on the AdS boundary can be extended into the interior.

This is joint work with Gustav Holzegel (Imperial College).