In this paper, we examine the functional forms of the potentials W(u,v,xA) that emerge from the Lagrangian of the pp-wave spacetime. To facilitate this investigation, Noether symmetries are employed as well as their linear combinations and subalgebras. We exploit the geometric fact that Noether point symmetries of geodesic Lagrangians are generated from the Homothetic algebra of spacetimes. Thus, we provide a complete analysis of the potentials of this spacetime, which are split into 14 isometry categories.

中文翻译：

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pp 波势函数：使用 Noether 对称性的完整研究

在本文中，我们研究了势的函数形式W(你,v,X一种)来自 pp 波时空的拉格朗日。为了促进这项研究，使用了 Noether 对称性以及它们的线性组合和子代数。我们利用几何事实，即测地拉格朗日的 Noether 点对称性是从时空的同位代数中产生的。因此，我们提供了对该时空潜力的完整分析，将其分为 14 个等距类别。