The conformal Einstein field equations and the local extension of future null infinity

Abstract: We make use of an improved existence result for the characteristic initial value problem for the conformal Einstein equations to show that given initial data on two null hypersurfaces $\mathcal{N}\star$ and $\mathcal{N}'\star$ such that the conformal factor (but not its gradient) vanishes on a section of $\mathcal{N}_\star$ one recovers a portion of null infinity. This result combined with the theory of the hyperboloidal initial value problem for the conformal Einstein field equations allows to show the semi-global stability of the Minkowski spacetime from characteristic initial data.