角动量通量的协变性与超平移不变性的三个谜题（附解答）
Three Puzzles with Covariance and Supertranslation Invariance of Angular Momentum Flux (with Solutions)
AI总结：
本文针对渐近平直时空中 Lorentz 荷通量的协变与超平移不变公式提出的三个谜题，给出协变公式以确定辅助自由度，并区分协变荷与正则荷的作用。
摘要：
我们描述并解决了在渐近平直时空中角动量及其他 Lorentz 荷通量的协变且超平移不变公式中出现的三个谜题：1）超平移不变性与协变性蕴含时空平移下的不变性；2）通量依赖于冗余的辅助自由度，而这些自由度无法在所有 Lorentz 参考系中都被设为零而不破坏 Lorentz 协变性；3）超平移不变的 Lorentz 荷不会生成由渐近度规的等距性所蕴含的 Bondi 质量方面的变换。在本信中，我们通过给出能明确确定辅助自由度的协变公式解决了前两个谜题，并通过解释协变荷与正则荷所发挥的不同作用阐明了最后一个谜题。我们的构造明确揭示了支撑当前文献中看似明确的结果的参考系选择。
英文摘要：
We describe and solve three puzzles arising in covariant and supertranslation-invariant formulas for the flux of angular momentum and other Lorentz charges in asymptotically flat spacetimes: 1) Supertranslation-invariance and covariance imply invariance under spacetime translations; 2) the flux depends on redundant auxiliary degrees of freedom that cannot be set to zero in all Lorentz frames without breaking Lorentz covariance; 3) supertranslation-invariant Lorentz charges do not generate the transformations of the Bondi mass aspect implied by the isometries of the asymptotic metric. In this letter, we solve the first two puzzles by presenting covariant formulas that unambiguously determine the auxiliary degrees of freedom and clarify the last puzzle by explaining the different role played by covariant and canonical charges. Our construction makes explicit the choice of reference frame underpinning seemingly unambiguous results presented in the current literature.
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