Intuitive Significance
The condition of asymptotic flatness is analogous to similar conditions in mathematics and in other physical theories. Such conditions say that some physical field or mathematical function is asymptotically vanishing in a suitable sense.
In general relativity, an asymptotically flat vacuum solution models the exterior gravitational field of an isolated massive object. Therefore, such a spacetime can be considered as examples of isolated systems in the sense in which this term is used in physics in general. (Isolated systems are ones in which exterior influences can be neglected.) Indeed, physicists rarely imagine a universe containing a single star and nothing else when they construct an asymptotically flat model of a star; rather, they are interested in modeling the interior of the star together with an exterior region in which gravitational effects due to the presence of other objects, such as "nearby" stars, can be neglected. Since typical distances between astrophysical bodies tend to be much larger than the diameter of each body, we often can get away with this idealization, which usually helps to greatly simplify the construction and analysis of solutions.
Read more about this topic: Asymptotically Flat Spacetime
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