We adapt Luk’s analysis of the characteristic initial value problem in general relativity to the asymptotic characteristic problem for the conformal Einstein field equations to demonstrate the local existence of solutions in a neighbourhood of the set on which the data are given. In particular, we obtain existence of solutions along a narrow rectangle along null infinity which, in turn, corresponds to an infinite domain in the asymptotic region of the physical spacetime. This result generalises work by Kannar on the local existence of solutions to the characteristic initial value problem by means of Rendall’s reduction strategy. In analysing the conformal Einstein equations we make use of the Newman–Penrose formalism and a gauge due to J. Stewart.

中文翻译：

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具有共形爱因斯坦场方程的特征初值问题的改进存在性

我们将 Luk 对广义相对论中特征初值问题的分析应用于保形爱因斯坦场方程的渐近特征问题，以证明在给出数据的集合的邻域中解的局部存在。特别是，我们沿着零无穷大的窄矩形获得解的存在性，而这又对应于物理时空渐近区域中的无限域。该结果概括了 Kannar 通过 Rendall 的约简策略对特征初值问题的解的局部存在性的工作。在分析共形爱因斯坦方程时，我们利用了 Newman-Penrose 形式主义和 J. Stewart 的规范。