The outgoing black-hole approximation problem for asymptotically flat vacuum solutions

An asymptotically flat solution of the vacuum Einstein equations is said to approximate $n$ outgoing black holes in a neighbourhood of future timelike infinity $i_+$. Outgoing black-hole approximation problem. There exists an asymptotically flat solution to the vacuum Einstein equations that approximates $n$ outgoing black holes in a neighbourhood of $i_+$. This is identified in the paper as an open problem in general relativity concerning the construction of localised objects emerging from future timelike infinity.