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BMS-supertranslation charges at the critical sets of null infinity

For asymptotically flat spacetimes, a conjecture by Strominger states that asymptotic BMS-supertranslations and their associated charges at past null infinity can be related to those at future null infinity via an antipodal map at spatial infinity. We analyse 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. We show that for a generic class of asymptotically Euclidean and regular initial data, BMS-supertranslation charges are not well-defined at the critical sets where null infinity meets spatial infinity 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 the critical sets are fully determined by the initial data and that the relation between the charges at past null infinity and those at future null infinity directly follows from our regularity condition. This is joint work with Mariem Magdy Ali Mohamed and Kartik Prabhu.

This is part of the Joint Online Mathematical Relativity Colloquium.