Title
Unique Continuation for Waves and Local AdS Rigidity
Abstract
In the context of holography, we would like to establish correspondence statements between asymptotically anti-de Sitter (aAdS) solutions of the Einstein-vacuum equations and suitable ‘data’ on the conformal boundary. To this end, progress has been made in the Riemannian (Biquard ‘08) and Stationary Lorentzian (Chruściel-Delay ‘11) cases, though there is still work to be done in the non-stationary case. We discuss recent unique continuation results for wave equations on aAdS backgrounds which lay the groundwork for progress in the non-stationary setting. In particular, we will see how these preliminary results already lead to a rigidity statement for locally AdS spacetimes based around conditions on the boundary data. This talk involves joint work with Arick Shao.
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