Starting from an action principle adapted to the Newman-Penrose formalism, we provide a self-contained derivation of BMS current algebra, which includes the generalization of the Bondi mass loss formula to all BMS generators. In the spirit of the Newman-Penrose approach, infinitesimal diffeomorphisms are expressed in terms of four scalars rather than a vector field. In this framework, the on-shell closed co-dimension two forms of the linearized theory associated with Killing vectors of the background are constructed from a standard algorithm. The explicit expression for the breaking that occurs when using residual gauge transformations instead of exact Killing vectors is worked out and related to the presymplectic flux.

中文翻译：

---

纽曼-彭罗斯形式主义背景下的 BMS 当前代数

从适用于 Newman-Penrose 形式主义的作用原理开始，我们提供了 BMS 当前代数的独立推导，其中包括将 Bondi 质量损失公式推广到所有 BMS 生成器。本着 Newman-Penrose 方法的精神，无穷小微分同胚用四个标量而不是矢量场表示。在该框架中，与背景的杀伤向量相关的线性化理论的壳上封闭共维两种形式是从标准算法构建的。当使用残差规范变换而不是精确的 Killing 向量时发生的破坏的显式表达式被计算出来并且与前辛通量相关。