  We present the argument that the past limit of the Trautman-Bondi mass is the
ADM mass under weak hypotheses on the decay of the metric towards spatial
infinity, without any smallness conditions on the initial data, assuming well
defined energy, momentum, center of mass and angular moment. Part of the proof
consists of a careful inspection of the proof of stability of Minkowski
space-time, which is sketched. This is complemented by an interior gluing
result for asymptotically flat initial data with well defined Poincar\'e
charges, which is proved in detail.
