Asymptotic symmetries in Bondi gauge and the sub-subleading soft graviton theorem

TL;DR

This paper explores the connection between asymptotic symmetries in Bondi gauge and soft graviton theorems, revealing new conserved charges linked to sub-subleading soft theorems in gravitational scattering.

Contribution

It identifies generalized superrotation symmetries and derives their conserved charges using the Noether procedure, connecting them to sub-subleading soft graviton theorems.

Findings

Conserved charges for generalized superrotations are derived.

A link between asymptotic symmetries and sub-subleading soft theorems is established.

The associated charges involve a combination of diffeomorphisms and metric transformations.

Abstract

We investigate asymptotic symmetries which preserve the Bondi gauge conditions but do not preserve the asymptotic falloff conditions for the metric near the null boundary, and their connection to soft graviton theorems for scattering amplitudes. These include generalized superrotation symmetries parameterized by a smooth vector field $Y^{A}$ obeying $D_{A}Y^{A} = 0$, for which we show that the associated conserved charge can be derived by applying the Noether procedure to the Einstein-Katz action. We also discuss the connection between asymptotic symmetries and the conserved charge associated with the sub-subleading soft theorem, and we find that in Bondi gauge this charge is generated by the combination of a diffeomorphism together with an extra transformation of the metric.