An asymptotically flat spacetime approaches Minkowski spacetime sufficiently far from isolated sources. At null infinity this is stated invariantly by requiring a smooth conformal completion whose boundary contains future and past null infinity.
A conformal completion embeds a physical spacetime into a manifold with boundary carrying a regular metric . Infinity is represented by with ; the causal character of each boundary component is determined by .
Future null infinity is the boundary reached by future-directed outgoing null geodesics in an asymptotically flat spacetime. In four dimensions it has topology under the standard asymptotic-flatness assumptions.
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Asymptotically flat spacetime is a concept in general relativity that describes the behavior of spacetime in regions that are far away from any gravitational sources, such as stars or black holes. In this context, "asymptotically flat" refers to the idea that as one moves far from the influence of mass and energy, the geometry of spacetime approaches that of flat Minkowski space, which is the simplest model of spacetime in special relativity.