The article aims to analyze a construction of charges (conserved quantities) for the gravity field in the (3 \(+\) 1) decomposition. The construction is based on (3 \(+\) 1) splitting of conformal Yano–Killing two-form. The splitting leads to charges, defined on Cauchy surface, which are combined from components of Weyl tensor and conformal Killing vector. The relations between the conserved quantities and its classical ADM counterparts are revisited. Asymptotic behavior of the conserved quantities is described. The charges are analyzed for a particular choice of initial data, among others, Bowen–York spinning black hole.

中文翻译：

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空间无穷处的准局域瞬时电荷渐近

本文旨在分析 (3 \(+\) 1) 分解中重力场的电荷（守恒量）构造。该构造基于 (3 \(+\) 1) 共形 Yano–Killing 两种形式的分裂。分裂导致在柯西表面上定义的电荷，这些电荷由外尔张量和保形 Killing 向量的分量组合而成。守恒量与其经典 ADM 对应物之间的关系被重新审视。描述了守恒量的渐近行为。针对特定的初始数据选择分析电荷，其中包括鲍文-约克旋转黑洞。