A Note on the Subleading Soft Graviton

TL;DR

This note demonstrates that the subleading soft graviton mode associated with superrotations can be encoded entirely in boundary data at null infinity, specifically through the subleading metric component $h_{zz}^{(0)}$ and its relation to $h_{zz}^{(-1)}$, within harmonic gauge. By deriving a conservation law and expressing the soft part of the superrotation charge as a boundary difference of asymptotic data, it builds a direct link between the subleading soft theorem and boundary observables. The spin memory, previously described in terms of bulk radiative data, is shown to correspond to a contour integral of the boundary field $\hat V^A$ between early and late times, further tying together soft theorems, memory effects, and asymptotic symmetries in a boundary-centric framework.

Abstract

We show that the soft part of the charge generating infinitesimal superrotations can be expressed, in harmonic gauge, in terms of metric components evaluated at the boundaries of null infinity that are subleading in a large radius expansion. We then recast the spin memory observable in terms of these boundary values.