超平移和超旋转
Hypertranslations and Hyperrotations
摘要：
研究了平坦空间中爱因斯坦引力的渐近对称性。我们用最近引进的特殊双零规范代替Bondi规范，其中$\mathscr{I}^{+}$和$\mathscr{I}^{-}$沿零方向逼近。我们发现四个新的功能价值的渐近超同胚超出熟悉的超平移和超旋转，这是相关的讨论有限的表面电荷。其中两个产生于$\mathscr{I}^{+}$附近$v$坐标的角度依赖性位移。我们称这些超平移和次引导超平移，在$\mathscr{I}^{-}$附近的$u$坐标中有类似的陈述。还有两个Diff $(S^2)$变换，我们称之为超旋转，它们是Virasoro超旋转的子导。在零坐标下的幂律衰减和球面上的标准度量的前导阶下，我们证明了这是其相关度量参数可以出现在（有限）表面电荷中的复同态的穷举列表.我们计算了Barnich-Troessaert括号下的渐近Killing向量的代数，并找到了BMS代数的四重无限推广。
英文摘要：
We study the asymptotic symmetries of Einstein gravity in flat space. Instead of Bondi gauge, we work with the recently introduced special double null gauge, in which $\mathscr{I}^{+}$ and $\mathscr{I}^{-}$ are approached along null directions. We find four new functions worth of asymptotic diffeomorphisms beyond the familiar supertranslations and superrotations, which are of relevance in discussions of finite surface charges. Two of these arise from angle-dependent shifts in the $v$-coordinate near $\mathscr{I}^{+}$. We call these hypertranslations and sub-leading hypertranslations, with analogous statements in the $u$-coordinate near $\mathscr{I}^{-}$. There are also two Diff$(S^2)$ transformations, which we call hyperrotations, that are sub-leading to the Virasoro superrotations. With power law fall-offs in the null coordinate and the standard metric on the sphere at leading order, we prove that this is the exhaustive list of diffeomorphisms whose associated metric parameters can show up in the (finite) surface charges. We compute the algebra of the asymptotic Killing vectors under the Barnich-Troessaert bracket, and find a four-fold infinite generalization of the BMS algebra.
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