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In the literature, there is often a distinction made between spacetimes that are asymptotically or asymptotically locally some other spacetime. For example, in holography, referring to some spaces that are asymptotically Anti-de Sitter (AAdS) or asymptotically locally Anti-de Sitter (AlAdS). What is the difference between both? When some space in AlAdS but not AAdS and how can we distinguish them?

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