ÃÛÌÒTV

In this talk, we establish corresondence properties for (massive and massless) waves on asymptotically AdS backgrounds. We show, roughly, that for a wave $\phi$ on this background, if $\phi$ and its first derivative vanish to high enough order (depending on the mass) on a sufficiently large but finite portion of infinity, then $\phi$ must also necessarily vanish in a small neighborhood of infinity. In particular, this establishes a correspondence between data for $\phi$ at infinity and the value of $\phi$ in the interior.

When available, we connect our results to the well-posedness theory: we show that trivial Dirichet and Neumann data at (a large enough portion of) infinity along with sufficient regularity implies vanishing in the interior. Finally, we discuss applications of this result to proving analogous correspondence properties for the full Einstein-vacuum equations.

This is joint work with Gustav Holzegel.