On asymptotic flatness

Starting with a few basic assumptions on the local asymptotic behavior of space-time and using Penrose's conformal technique the asymptotic behavior of both the physical and unphysical metric is obtained in a Bondi-type coordinate system. The space-times under consideration are not necessarily empty in the asymptotic region nor are they necessarily asymptotically flat. However, they do have the usual falloff behavior as one goes out toward infinity in a given null direction. The assumptions made in this paper and the resultant metrics are compared with those of Persides in his recent paper on the definition of asymptotic flatness.