Using the Newman-Penrose formalism we study the characteristic initial value problem in vacuum General Relativity. We work in a gauge suggested by Stewart, and following the strategy taken in the work of Luk, demonstrate local existence of solutions in a neighbourhood of the set on which data are given. These data are given on intersecting null hypersurfaces. Existence near their intersection is achieved by combining the observation that the field equations are symmetric hyperbolic in this gauge with the results of Rendall. To obtain existence all the way along the null-hypersurfaces themselves, a bootstrap argument involving the Newman-Penrose variables is performed.

中文翻译：

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重温真空爱因斯坦场方程的特征初值问题

我们使用 Newman-Penrose 形式主义研究真空广义相对论中的特征初值问题。我们在 Stewart 建议的量规中工作，并遵循 Luk 工作中采取的策略，证明在给出数据的集合的邻域中解的局部存在。这些数据是在相交的零超曲面上给出的。通过将观察到的场方程在该规范中是对称双曲线的与 Rendall 的结果相结合，可以实现它们的交点附近的存在。为了获得零超曲面本身的存在性，执行涉及 Newman-Penrose 变量的引导参数。