Asymptotic structure with vanishing cosmological constant

This is the first of two papers devoted to asymptotic structure space-time in presence a non-negative cosmological constant $\Lambda$. paper concerned with case $\Lambda =0$. Our approach fully based on tidal nature gravitational field and therefore `tidal energies' built Weyl curvature. In particular, we use (radiant) supermomenta computed from rescaled tensor at infinity provide novel characterisation radiation escaping from, or entering into, space-time. new criterion easy implement shown be equivalent classical one news tensor. One its virtues that formulation can easily adapted $\Lambda>0$ covered second paper. We derive general energy-momentum-loss formulae including matter terms all factors associated choices arbitrary foliation super-translation. also revisit present full reformulation traditional peeling behaviour neat geometrical construction leads, an alignment accordance criterion.