Description
In physics, the notion of isolated system is a crucial one. However, the definition of this concept in the context of general relativity contains some subtleties. One generally proceeds by asking the boundary of the space-time (obtained through conformal compactification) to share some similarities with the one of the Minkowski space-time, $\textit{i.e.}$ the space-time of an empty and flat universe. This powerful idea from Penrose, which dates back to the 60's, enables computations at infinity and has been extensively used in the litterature. However, while it works very well on some part of infinity called null infinity, it is unable to describe correctly some other parts, space and time-like infinity. After having reviewed Penrose's formalism and the structures it induces on null-infinity, we will see how one can construct analogues of these structures on space and time-like infinity.
