# The bulk-boundary correspondence for the Einstein equations in asymptotically Anti-de Sitter spacetimes

@inproceedings{Holzegel2022TheBC, title={The bulk-boundary correspondence for the Einstein equations in asymptotically Anti-de Sitter spacetimes}, author={Gustav H. Holzegel and Arick Shao}, year={2022} }

In this paper, we consider vacuum asymptotically anti-de Sitter spacetimes (M , g) with conformal boundary (I , g). We establish a correspondence, near I , between such spacetimes and their conformal boundary data on I . More specifically, given a domain D ⊂ I , we prove that the coefficients g = g and g (the undetermined term, or stress energy tensor) in a FeffermanGraham expansion of the metric g from the boundary uniquely determine g near D , provided D satisfies a generalised null convexity…

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