AI 中文总结
该研究构建零无穷远克尔软 dressing 对应的内禀框架字典，利用 $w_{1+\infty}$ 型代数确定克尔多极塔，解释其在黑洞散射中产生位移、自旋等记忆的物理作用。
AI 中文摘要
我们构造与克尔选取的软 dressing 相关联的、由电荷生成的内禀/正则框架字典。从VV超平移出发，我们将高自旋问题表述为零无穷远处的一个逆问题：由适配宇称的极大纵向标量 $\chi^{(s)}_t$ 构建的软核 $\mathcal{K}^{(s,0)}_{AB}[t]$，与通用软贡献的克尔选取指数投影相匹配，从而确定生成元 $t^{A_1\cdots A_s}$ 的一个宇称分量；螺旋度共轭确定了具体是哪一个：指数源满足 $\overline{S^{(s)}_{+,{\rm exp}}}=(-1)^sS^{(s)}_{-,{\rm exp}}$，因此该塔在偶级时确定源的电投影，在奇级时确定磁投影，与克尔质量和电流矩的交替特性相匹配；对于自旋对齐的情况，该投影是完备的，我们以闭式形式求解该塔。该方案在领头阶重现VV超平移，并在次领头阶确定光滑广义BMS矢量的旋度而非散度。匹配的物理原因在于：同一指数软因子是Guevara–Ochirov–Vines自旋三点算符的经典极限，且生成克尔多极塔。我们解释了相应的硬流电荷，并展示其外态作用如何给出软定理的沃德表示。$T^*S^2$上的多项式泊松代数（带有局部 $w_{1+\infty}$ 型约化）随后作用于这些改变框架的生成元；该代数并不仅在克尔选取数据上闭合。这阐明了克尔黑洞散射中类 $w_{1+\infty}$ 结构的物理作用：它移动内禀/正则字典。其可观测印记始于 $s=0$ 时的位移记忆和 $s=1$ 时的自旋记忆，随后是更高阶的电和磁记忆矩。
英文摘要
We construct the charge-generated intrinsic/canonical frame dictionary associated with the Kerr-selected soft dressing. Starting from the VV supertranslation, we formulate the higher-spin problem as an inverse problem at null infinity: the soft kernel ${\mathcal K}^{(s,0)}_{AB}[t]$, built from the parity-adapted maximally longitudinal scalar $χ^{(s)}_t$, is matched to the Kerr-selected exponentiating projection of the universal soft contribution, thereby determining one parity component of the generator $t^{A_1\cdots A_s}$. Helicity conjugation fixes which one: the exponentiating source obeys $\overline{S^{(s)}_{+,{\rm exp}}}=(-1)^sS^{(s)}_{-,{\rm exp}}$, so the tower fixes the electric projection of the source at even levels and the magnetic projection at odd ones, matching the alternation of the Kerr mass and current moments; for aligned spin the projection is exhaustive and we solve the tower in closed form. The prescription reproduces the VV supertranslation at leading order and fixes the curl, not the divergence, of a smooth generalized-BMS vector at subleading order. The reason for the matching is physical: the same exponentiating soft factor is the classical limit of the Guevara--Ochirov--Vines spinning three-point operator and generates the Kerr multipole tower. We explain the corresponding hard flux charges and show how their external-state action gives the Ward representation of the soft theorem. The polynomial Poisson algebra on $T^\ast S^2$, with local $w_{1+\infty}$-type reductions, then acts on these frame-changing generators; it does not close on the Kerr-selected data alone. This gives the physical role of the $w_{1+\infty}$-like structure in Kerr black-hole scattering: it moves the intrinsic/canonical dictionary. Its observable imprint begins with displacement memory at $s=0$ and spin memory at $s=1$, followed by higher electric and magnetic memory moments.
Comments92 pages
