An initial data characterization for vacuum pp-wave spacetimes in dimension four is constructed. This is a vacuum initial data set plus some extra conditions guaranteeing that the data development is a subset of a vacuum pp-wave. Some of the extra conditions only depend on the same quantities used to construct the vacuum initial data, namely the first and the second fundamental forms while others are related to a conformal Killing initial data characterization (CKID).

中文翻译：

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pp-wave 初始数据

构建了四维真空pp波时空的初始数据表征。这是一个真空初始数据集加上一些额外的条件，保证数据开发是真空pp波的一个子集。一些额外条件仅取决于用于构建真空初始数据的相同数量，即第一和第二基本形式，而其他条件与保形 Killing 初始数据表征(CKID) 有关。