Teleparallel gravity at null infinity

TL;DR

This paper investigates teleparallel gravity as an alternative formulation of general relativity at null infinity, focusing on encoding Goldstone modes associated with BMS symmetries within the flat connection framework.

Contribution

It introduces a novel way to encode Goldstone modes in teleparallel gravity, connecting asymptotic symmetries with the flat connection in the covariant phase space.

Findings

Goldstone modes can be encoded in the flat connection of teleparallel gravity

The approach links BMS symmetries with the covariant phase space structure

Implications for the Wald-Zoupas prescription are discussed

Abstract

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 (BMS) 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.