Logarithmic asymptotic flatness

We present a general family of asymptotic solutions to Einstein's equation which are asymptotically flat but do not satisfy the peeling theorem. Near scri, the Weyl tensor obeys a logarithmic asymptotic flatness condition and has a partial peeling property. The physical significance of this asymptotic behavior arises from a quasi-Newtonian treatment of the radiation from a collapsing dust cloud. Practically all the scri formalism carries over intact to this new version of asymptotic flatness.