For asymptotically flat spacetimes, a conjecture by Strominger states that asymptotic BMS-supertranslations and their associated charges at past null infinity I− can be related to those at future null infinity I+ via an antipodal map at spatial infinity i0. We analyze the validity of this conjecture using Friedrich’s formulation of spatial infinity, which gives rise to a regular initial value problem for the conformal field equations at spatial infinity. A central structure in this analysis is the cylinder at spatial infinity I representing a blow-up of the standard spatial infinity point i0 to a 2-sphere. The cylinder I touches past and future null infinities I± at the critical sets I±. We show that for a generic class of asymptotically Euclidean and regular initial data, BMS-supertranslation charges are not well-defined at I± unless the initial data satisfies an extra regularity condition. We also show that given initial data that satisfy the regularity condition, BMS-supertranslation charges at I± are fully determined by the initial data and that the relation between the charges at I− and those at I+ directly follows from our regularity condition.

中文翻译：

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BMS-超平移在零无穷大的临界集处收费

对于渐近平坦时空，Strominger 的猜想指出，过去零无穷大 I− 处的渐近 BMS 超平移及其相关电荷可以通过空间无穷大 i0 处的对映图与未来零无穷大 I+ 处的电荷相关。我们使用弗里德里希的空间无穷远公式来分析该猜想的有效性，这引起了空间无穷远共形场方程的常规初值问题。此分析中的中心结构是空间无穷远 I 处的圆柱体，表示将标准空间无穷远点 i0 放大为 2 球体。圆柱体 I 在临界集合 I± 处接触过去和未来的零无穷大 I±。我们表明，对于一类渐近欧几里得和规则初始数据，BMS 超平移电荷在 I± 处没有明确定义，除非初始数据满足额外的规则性条件。我们还表明，给定满足规律性条件的初始数据，I± 处的 BMS 超平移电荷完全由初始数据决定，并且 I− 处的电荷与 I+ 处的电荷之间的关系直接遵循我们的规律性条件。