发表机构
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh（爱丁堡大学数学学院与麦克斯韦数学科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用Carroll几何和共形代数规范联络，通过$K$-曲率分类渐近平坦时空，并揭示其与Weyl张量、Carroll助推反常及Bondi损失方程的联系。
AI 中文摘要
我们考虑近未来零无穷远的四维渐近平坦真空时空，并赋予其最一般的允许Carroll几何。我们证明，近边界径向展开（至某一阶）可以用通过规范共形Carroll代数得到的联络来组织。在此规范过程中，唯一非零的曲率是与特殊共形生成元相关的曲率，我们称之为$K$-曲率。这些$K$-曲率的消失定义了一个渐近真空时空，我们利用这一点构造了真空（软）剪切的边界（即Carroll）协变表达式，该表达式用两个边界Carroll标量场表示。$K$-曲率在Carroll助推下以层级方式相互变换。这导致了对4类时空的分类：真空、强非辐射、弱非辐射和辐射时空。我们证明，$K$-曲率对应于Weyl张量在$1/r$展开中领先阶的10个分量中的5个。我们还观察到，其中一个$K$-曲率等于最近发现的Carroll助推反常。最后，我们证明，边界能量-动量-新闻复合体的Bondi损失方程可以转化为涉及另一个能量-动量张量的形式，该张量具有零能量通量且无迹，其非守恒完全由$K$-曲率捕获。BMS流可以通过将后一个能量-动量张量与Carroll共形Killing矢量收缩而获得。
英文摘要
We consider 4-dimensional asymptotically flat vacuum spacetimes near future null infinity endowed with the most general allowable Carroll geometry. We show that the near-boundary radial expansion (to a certain order) can be organised in terms of connections that can be obtained by gauging the conformal Carroll algebra. The only non-vanishing curvatures in this gauging procedure are those that are associated with the special conformal generators and we will refer to these as the $K$-curvatures. The vanishing of these $K$-curvatures defines an asymptotic vacuum spacetime and we use this to construct a boundary (i.e. Carroll) covariant expression for the vacuum (soft) shear in terms of two boundary Carroll scalar fields. The $K$-curvatures transform in a hierarchical fashion into one another under Carroll boosts. This leads to a classification of 4 types of spacetimes: vacuum, strongly and weakly non-radiative, and radiative spacetimes. It is shown that the $K$-curvatures correspond to 5 of the 10 Weyl tensor components at leading order in their $1/r$ expansion. We furthermore observe that one of the $K$-curvatures is equal to the recently found Carroll boost anomaly. Finally, we show that the Bondi loss equations for the boundary energy-momentum-news complex can be cast into a form involving another energy-momentum tensor with vanishing energy flux that is traceless and whose non-conservation is entirely captured by the $K$-curvatures. The BMS currents can be obtained by contracting this latter energy-momentum tensor with a Carroll conformal Killing vector.
Comments76 pages, 6 appendices
