General future asymptotically flat spacetimes

The standard notions of asymptotically flat spacetimes have been challenged by the examples found by Isaacson, Welling and Winicour (1984), which show logarithmic asymptotic behaviour. Here, a geometrical definition of general future asymptotically flat (GeFAF) spacetimes is introduced, and its implications are systematically studied throughout the paper. Conformal techniques are used, but no reference to field equations is made. In particular logarithmic behaviour is studied. For the general GeFAF case it is deduced that the radiation fields always behave like 1/r asymptotically.