Existence of radiating Einstein-Maxwell solutions which are C ∞ on all of I ⁺ and I $

The authors give a prescription for constructing C infinity solutions of the Einstein-Maxwell constraint equations on R 3 which are close to flat initial data and which are exactly vacuum Schwarzschild initial data outside of a compact region. They use a generalisation of a theorem due to Friedrich (1988) to prove that the maximal evolution of these initial data sets are C infinity -conformally extendible to future and past null and timelike infinity, I + , i + , I - and i - . This establishes the existence of radiating solutions which are smoothly asymptotically flat in both the past and future.