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We adapt Luk's analysis of the characteristic initial value problem inGeneral Relativity to the asymptotic characteristic problem for the conformalEinstein field equations to demonstrate the local existence of solutions in aneighbourhood of the set on which the data are given. In particular, we obtainexistence of solutions along a narrow rectangle along null infinity which, inturn, corresponds to an infinite domain in the asymptotic region of thephysical spacetime. This result generalises work by K\'ann\'ar on the localexistence of solutions to the characteristic initial value problem by means ofRendall's reduction strategy. In analysing the conformal Einstein equations wemake use of the Newman-Penrose formalism and a gauge due to J. Stewart.

Improved existence for the characteristic initial value problem with the conformal Einstein field equations