Given identical boundary data near infinity, two solutions of the AdS-Einstein-Maxwell equations must agree near that boundary, provided the boundary region satisfies a null-convexity condition.
Rigidity Results in General Relativity: a Review
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In this survey we review the progress made in the last ten years in understanding the Black Hole Rigidity problem in the setting of smooth spacetimes. We review both local and global results and discuss the main mathematical ideas behind them.
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Near-Boundary Asymptotics and Unique Continuation for the AdS--Einstein--Maxwell System
Given identical boundary data near infinity, two solutions of the AdS-Einstein-Maxwell equations must agree near that boundary, provided the boundary region satisfies a null-convexity condition.