Why is asymptotic flatness a good assumption for solving Einstein's field equations? Intuitively it makes sense to me but I am looking for a formal justification. (By asymptotic flatness I mean that the metric is Minkowskian at large distances.)
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It is impossible to solve EFE completely: we are seeking a solution, not all solutions.
Also, we want a special solution satisfying the following: the gravitational effects of a star/black hole/etc. have be negligible at huge distances, because the effects of distant attractors doesn't play a major role in our life (indeed, experimentalists put major effort into discovering these objects).
In mathematical language this requirement is exactly asymptotic flatness.
Prof. Legolasov
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1Well, it has to be asymptotically a cosmological solution, not necessarily flat. Asymptotic flatness is the simplest but it's not necessarily the most realistic of assumptions. – Slereah Jan 10 '17 at 11:34
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@Slereah good point, but the context of the question is IMO clear: OP wants to know why we impose asymptotic flatness for gravitating-center kinds of solutions. – Prof. Legolasov Jan 10 '17 at 11:39