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

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.