Teleparallel gravity at null infinity

Four-dimensional asymptotically flat spacetimes have been central to recent developments in infrared physics. Gravitational waves reaching the asymptotic boundary reveal an infinite-dimensional symmetry group known as the Bondi-Metzner-Sachs group. The vacuum structure breaks this symmetry, giving rise to Goldstone modes that play a pivotal role in the analysis of scattering amplitudes. However, these modes must be added to the phase space of the metric formulation. In this work, we explore an alternative formulation of general relativity, teleparallel gravity, which is dynamically equivalent to the standard metric description in the bulk. This framework relies on a tetrad field to encode the gravitational degrees of freedom and a flat connection to represent inertial effects. Leveraging this decomposition, we propose a novel encoding of the Goldstone modes within the flat connection. We examine the implications of this approach in the covariant phase space framework, focusing on the symplectic potential and its connection to the Wald-Zoupas prescription.