标题： GHP形式主义中的积分 III：作为“最优情况”示例的所有共形平坦辐射度规的寻找 显示英文标题

标题： Integration in the GHP formalism III: Finding all conformally flat radiation metrics as an example of an `optimal situation'

摘要： 赫尔德在GHP形式主义中提出了一种积分过程，该过程围绕四个实数、功能独立的零权标量构建。他建议，当形式主义直接提供此类四个标量的全部数量时，这种过程在“最佳情况”下会特别简单；没有任何凯尔文矢量的时空就是这种情况。威尔斯最近获得了一个度规，他声称这是唯一一个不是平面波的共形平坦纯辐射度规；该度规已被库特拉斯证明通常不包含凯尔文矢量。因此，作为GHP积分过程的一个简单示例，我们系统地获得了共形平坦纯辐射度规的完整类。我们的结果表明，不是平面波的共形平坦纯辐射度规是一个比威尔斯获得的更大的类。 显示英文摘要

摘要： Held has proposed an integration procedure within the GHP formalism built around four real, functionally independent, zero-weighted scalars. He suggests that such a procedure would be particularly simple for the `optimal situation', when the formalism directly supplies the full quota of four scalars of this type; a spacetime without any Killing vectors would be such a situation. Wils has recently obtained a metric which he claims is the only conformally flat, pure radiation metric which is not a plane wave; this metric has been shown by Koutras to admit no Killing vectors, in general. Therefore, as a simple illustration of the GHP integration procedure, we obtain systematically the complete class of conformally flat, pure radiation metrics. Our result shows that the conformally flat, pure radiation metrics, which are not plane waves, are a larger class than Wils has obtained.