Characteristic Initial Data and Smoothness of Scri. I. Framework and Results

Abstract

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.