We exhibit a Hamiltonian formulation, both for electromagnetism and gravitation, in which it is not required that the Bondi “news” vanish but only that the incoming news be equal to the outgoing ones. This requirement is implemented by defining the fields on a two–sheeted hyperbolic surface, which we term “the hourglass.” It is a spacelike deformation of the complete light cone. On it, one approaches asymptotically (null) past and future infinity while remaining at a fixed (hyperbolic) time, by going to large spatial distances on its two sheets. The Hamiltonian formulation and—in particular—a conserved angular momentum, can only be constructed if one brings in both the electric and magnetic Bondi-Metzner-Sachs (BMS) charges together with their canonically conjugate “memories.” This reveals a close interplay between the BMS and electric-magnetic duality symmetries.

• Received 17 May 2019
• Accepted 8 January 2020

DOI:https://doi.org/10.1103/PhysRevD.101.044003