Characteristic initial data and smoothness of Scri. I. Framework and   results
  We analyze the Cauchy problem for the vacuum Einstein equations with data on a complete light-cone in an asymptotically Minkowskian space-time. We provide conditions on the free initial data which guarantee existence of global solutions of the characteristic constraint equations. We present necessary-and-sufficient conditions on characteristic initial data in $3+1$ dimensions to have no logarithmic terms in an asymptotic expansion at null infinity. 
Piotr T. Chru\'sciel, Tim-Torben Paetz
gr-qc