The partial Bondi gauge: Gauge fixings and asymptotic charges

TL;DR

This work extends the analysis of asymptotic symmetries in gravity by focusing on the partial Bondi gauge, which generalizes Bondi–Sachs and Newman–Unti coordinates. By allowing a fluctuating boundary metric, the authors uncover two additional asymptotic charges tied to free traces in the angular metric, realized under specific complete gauge fixings (differential NU/BS gauges) and shown to survive in the Kerr and NU limits. They provide explicit expressions for bare and renormalized charges, demonstrate their consistency with GBMS in limiting cases, and analyze the charge algebra under different brackets, including a field-space-covariant Koszul bracket. The results illuminate how gauge choices and boundary data shape the asymptotic symmetry structure, with implications for holography, corner symmetries, and the interpretation of gravitational fluxes at null infinity.

Abstract

In the companion paper [SciPost Phys. 13, 108 (2022), arXiv:2205.11401 [hep-th]] we have studied the solution space at null infinity for gravity in the partial Bondi gauge. This partial gauge enables to recover as particular cases and among other choices the Bondi-Sachs and Newman-Unti gauges, and to approach the question of the most general boundary conditions and asymptotic charges in gravity. Here we compute and study the asymptotic charges and their algebra in this partial Bondi gauge, by focusing on the flat case with a varying boundary metric $δq_{AB}\neq0$. In addition to the super-translations, super-rotations, and Weyl transformations, we find two extra asymptotic symmetries associated with non-vanishing charges labelled by free functions in the solution space. These new symmetries arise from a weaker definition of the radial coordinate and switch on traces in the transverse metric. We also exhibit complete gauge fixing conditions in which these extra asymptotic symmetries and charges survive. As a byproduct of this calculation we obtain the charges in Newman-Unti gauge, in which one of these extra asymptotic charges is already non-vanishing. We also apply the formula for the charges in the partial Bondi gauge to the computation of the charges for the Kerr spacetime in Bondi coordinates.