引力散射、辐射反应和Bondi规范模糊性中的Angular momentum损失
Angular momentum loss in gravitational scattering, radiation reaction, and the Bondi gauge ambiguity
摘要：
最近，Damour计算了辐射对引力散射的反应，作为对角动量损失的（线性）响应，他发现在引力常量中是${\cal O}(G^2)$。这是一个难题，因为任何振幅计算都将产生能量和角动量损失，仅从${\cal O}(G^3)$开始。另一个令人困惑的问题是，所产生的辐射反应，即${\cal O}(G^3)$，仍然是正确的，并通过许多直接计算得到证实。我们把这些困惑归因于BMS在定义角动量时的模糊性。角动量的损失是从ADM值中计算出来的，因此，应该在所谓的正则规范中在BMS变换下计算，其中邦迪角动量的遥远过去极限与ADM角动量重合。该计算正确地给出了${\cal O}(G^3)$损失。另一方面，我们引入了一个规范，其中的邦迪光锥渐近趋于那些从质心世界线发出的。我们发现该规范中的角动量通量恰好是Damour在辐射反应结果中所用的角动量通量。我们称这种新的规范为“内在的”，并认为，虽然正确的角动量通量是在正则规范计算，任何力学计算的规范依赖量-如角动量-给出的结果在内在的规范。因此，在线性响应公式中应使用此量规。这解决了难题，并建立了内在力学计算和邦迪形式主义之间的对应关系。
英文摘要：
Recently, Damour computed the radiation reaction on gravitational scattering as the (linear) response to the angular momentum loss which he found to be of ${\cal O}(G^2)$ in the gravitational constant. This is a puzzle because any amplitude calculation would produce both energy and angular momentum losses starting only at ${\cal O}(G^3)$. Another puzzle is that the resultant radiation reaction, of ${\cal O}(G^3)$, is nevertheless correct and confirmed by a number of direct calculations. We ascribe these puzzles to the BMS ambiguity in defining angular momentum. The loss of angular momentum is to be counted out from the ADM value and, therefore, should be calculated in the so-called canonical gauge under the BMS transformations in which the remote-past limit of the Bondi angular momentum coincides with the ADM angular momentum. This calculation correctly gives the ${\cal O}(G^3)$ loss. On the other hand, we introduce a gauge in which the Bondi light cones tend asymptotically to those emanating from the center of mass world line. We find that the angular momentum flux in this gauge is precisely the one used by Damour for his radiation reaction result. We call this new gauge "intrinsic" and argue that, although the correct angular momentum flux is to be computed in the canonical gauge, any mechanical calculation of gauge-dependent quantities -- such as angular momentum -- gives the result in the intrinsic gauge. Therefore, it is this gauge that should be used in the linear response formula. This solves the puzzles and establishes the correspondence between the intrinsic mechanical calculations and the Bondi formalism.
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