引力两体散射中的角动量平衡：通量、记忆与超平移不变性
Angular momentum balance in gravitational two-body scattering: Flux, memory, and supertranslation invariance
AI总结：
针对引力两体散射角动量通量的参考系歧义及 QFT 结果不一致问题，本文区分 Bondi 角动量与机械角动量，提出含辐射项和静态项的全阶超平移不变平衡定律。
摘要：
两个谜题持续困扰着我们对引力两体散射中角动量平衡的理解。首先，由于 Bondi 角动量 $J$ 的标准定义存在超平移歧义，已有研究表明，当相应的通量 $F_J$ 按牛顿常数 $G$ 的幂次展开时，根据参考系选择的不同，它可能从 $O(G^2)$ 或 $O(G^3)$ 开始。这自然引出了一个问题：通量的 $O(G^2)$ 部分是否具有物理意义。第二个谜题涉及最近利用量子场论发展出的一组计算该通量的新方法。有些令人惊讶的是，研究发现这些方法通常与 $F_J$ 的标准公式不一致，只有在双星的质心系中除外。本文中，我们表明这两个谜题的解决都在于对 $J$ 的谨慎解释：一般而言，Bondi 角动量 $J$ 并不等于双星的机械角动量 $\mathcal{J}$，而后者才是真正受关注的量。相反，它是 $\mathcal{J}$ 与一个涉及引力场剪切的额外部分之和。通过分离这些贡献，我们得到了一条新的平衡定律，该定律在 $G$ 的所有阶上均准确，它将机械角动量的总损失 $Δ_\mathcal{J}$ 等同于一个辐射项与一个静态项之和，其中辐射项总是从 $O(G^3)$ 开始，静态项总是从 $O(G^2)$ 开始。我们证明这些项中的每一项都在超平移下保持不变，并且发现 $Δ_\mathcal{J}$ 在所有 Bondi 参考系中至少到 $O(G^2)$ 都与量子场论的结果相符。文中还讨论了我们的结果与其他关于角动量超平移不变定义的提议之间的联系。
英文摘要：
Two puzzles continue to plague our understanding of angular momentum balance in the context of gravitational two-body scattering. First, because the standard definition of the Bondi angular momentum $J$ is subject to a supertranslation ambiguity, it has been shown that when the corresponding flux $F_J$ is expanded in powers of Newton's constant $G$, it can start at either $O(G^2)$ or $O(G^3)$ depending on the choice of frame. This naturally raises the question as to whether the $O(G^2)$ part of the flux is physically meaningful. The second puzzle concerns a set of new methods for computing the flux that were recently developed using quantum field theory. Somewhat surprisingly, it was found that they generally do not agree with the standard formula for $F_J$, except in the binary's center-of-mass frame. In this paper, we show that the resolution to both of these puzzles lies in the careful interpretation of $J$: Generically, the Bondi angular momentum $J$ is \emph{not} equal to the mechanical angular momentum $\mathcal{J}$ of the binary, which is the actual quantity of interest. Rather, it is the sum of $\mathcal{J}$ and an extra piece involving the shear of the gravitational field. By separating these contributions, we obtain a new balance law, accurate to all orders in $G$, that equates the total loss in mechanical angular momentum $Δ_\mathcal{J}$ to the sum of a radiative term, which always starts at $O(G^3)$, and a static term, which always starts at $O(G^2)$. We show that each of these terms is invariant under supertranslations, and we find that $Δ_\mathcal{J}$ matches the result from quantum field theory at least up to $O(G^2)$ in all Bondi frames. The connection between our results and other proposals for supertranslation-invariant definitions of the angular momentum is also discussed.
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