Bondi-Metzner-Sachs invariance and electric-magnetic duality

Abstract

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 lightcone. 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 BMS charges, together with their canonically conjugate "memories". This reveals a close interplay between the BMS and electric-magnetic duality symmetries.

arXiv comment14 pages, 3 figures

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Cited by in corpus (6)

• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Geometric action for extended Bondi-Metzner-Sachs group in four dimensions
• Boundary conditions for General Relativity in three-dimensional spacetimes, integrable systems and the KdV/mKdV hierarchies
• Source and Response Soft Charges for Maxwell Theory on $Ad{S}_d$
• On the covariant formulation of gauge theories with boundaries
• Asymptotic symmetries in Carrollian theories of gravity