AI 中文总结
研究守恒引力荷在渐近AdS和渐近平坦设定下的等价曲率通量表示，通过特定无散四阶张量及反对称庞加莱基灵势构造公式，重现相关荷，检查归一化，指出非最大对称背景下的情况。
AI 中文摘要
守恒引力荷通常表示为度规微扰及其一阶导数的表面积分。我们表明，在通常的渐近反德西特（AdS）和渐近平坦设定中，标准荷允许等价的线性化曲率通量表示。该构造使用一个无散的四阶张量，其迹与宇宙学爱因斯坦张量成比例。在最大对称AdS背景下，它重现了阿博特 - 德塞尔（Abbott-Deser）荷的已知曲率表示。渐近平坦构造不是通过简单的$\Lambda \rightarrow 0$极限得到，因为平移的基灵二形式消失。我们引入一个反对称庞加莱基灵势。一个适应代数比安基恒等式的代表性基灵势将线性化爱因斯坦流转化为全散度并产生单个曲率通量公式。其平移部分重现ADM能量 - 动量，在四维中其洛伦兹部分在标准雷杰 - 泰特尔鲍姆（Regge-Teitelboim）衰减和宇称条件下重现角动量以及推进/质心荷。对史瓦西、加速史瓦西和克尔数据明确检查了归一化。在非最大对称爱因斯坦背景下，背景外尔曲率产生额外项，所以最大对称构造不能直接扩展到纯余维二曲率通量公式。
英文摘要
Conserved gravitational charges are commonly expressed as surface integrals of the metric perturbation and its first derivatives. We show that, in the usual asymptotically AdS and asymptotically flat settings, the standard charges admit equivalent representatives as fluxes of linearized curvature. The construction uses a divergence-free rank-four tensor whose trace is proportional to the cosmological Einstein tensor. On a maximally symmetric AdS background, it reproduces the known curvature representation of the Abbott-Deser charges. The asymptotically flat construction is not obtained by taking a naive $Λ\rightarrow 0$ limit, since the Killing two-form vanishes for translations. We instead introduce an antisymmetric Poincaré Killing potential. A representative Killing potential adapted to the algebraic Bianchi identity converts the linearized Einstein current into a total divergence and yields a single curvature-flux formula. Its translation sector reproduces the ADM energy--momentum, while in four dimensions its Lorentz sector reproduces the angular momentum and boost/center-of-mass charges under the standard Regge-Teitelboim falloff and parity conditions. The normalization is checked explicitly for Schwarzschild, boosted Schwarzschild, and Kerr data. On non-maximally symmetric Einstein backgrounds, background Weyl curvature generates additional terms, so the maximally symmetric construction does not directly extend to a pure codimension-two curvature-flux formula.
Comments37 pages, 1 figure, references added
