BMS-supertranslation charges at the critical sets of null infinity

Abstract

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.