Formal Definitions
A manifold M is asymptotically simple if it admits a conformal compactification such that every null geodesic in M has a future and past endpoints on the boundary of .
Since the latter excludes black holes, one defines a weakly asymptotically simple manifold as a manifold M with an open set U⊂M isometric to a neighbourhood of the boundary of, where is the conformal compactification of some asymptotically simple manifold.
A manifold is asymptotically flat if it is weakly asymptotically simple and asymptotically empty in the sense that its Ricci tensor vanishes in a neighbourhood of the boundary of .
Read more about this topic: Asymptotically Flat Spacetime
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