Unique continuation from infinity in asympotically Anti-de Sitter spacetimes II: Non-static boundaries

Abstract

We generalize our unique continuation results recently established for a class of linear and nonlinear wave equations ${\square }_g\varphi +\sigma \varphi =\mathcal{G}(\varphi ,\partial \varphi )$ 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.

45 pages. Newest version incorporated changes from referee comments and fixed minor typos

References in corpus (2)

• On the uniqueness and global dynamics of AdS spacetimes
• Non-equilibrium dynamics and $Ad{S}_4$ Robinson-Trautman

Cited by in corpus (7)

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• Null Geodesics and Improved Unique Continuation for Waves in Asymptotically Anti-de Sitter Spacetimes
• The bulk-boundary correspondence for the Einstein equations in asymptotically Anti-de Sitter spacetimes
• A mechanism for holography for non-interacting fields on anti-de Sitter spacetimes
• A gauge-invariant unique continuation criterion for waves in asymptotically Anti-de Sitter spacetimes
• The Near-Boundary Geometry of Einstein-Vacuum Asymptotically Anti-de Sitter Spacetimes
• Killing boundary data for anti-de Sitter-like spacetimes