# Bondi-Metzner-Sachs invariance and electric-magnetic duality

## TL;DR

This paper develops a Hamiltonian framework for electromagnetism and gravity that incorporates BMS invariance and electric-magnetic duality by using a novel hyperbolic surface approach, revealing deep symmetry connections.

## Contribution

It introduces a hyperbolic 'hourglass' surface for Hamiltonian formulation, unifying BMS invariance with electric-magnetic duality in electromagnetism and gravity.

## Key findings

- Hamiltonian formulation on hyperbolic surface without vanishing news
- Conserved angular momentum including electric and magnetic BMS charges
- Revealed interplay between BMS symmetry 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.