On symmetries of gravitational on-shell boundary action at null infinity

TL;DR

This paper analyzes the gravitational boundary action at null infinity, fixing ambiguities and connecting it to soft theorems and symmetries in asymptotically flat spacetimes.

Contribution

It introduces a method to fix corner ambiguities in the boundary action using on-shell amplitude constraints and extends the symmetry framework to include an infinite tower of Goldstone modes.

Findings

Fixes corner ambiguities using on-shell amplitude constraints.

Derives subleading soft graviton theorem from the on-shell action.

Proposes an infinite tower of Goldstone modes related to extended BMS symmetries.

Abstract

We revisit the gravitational boundary action at null infinity of asymptotically flat spacetimes. We fix the corner ambiguities in the boundary action by using the constraint that (exponential of) the on-shell action leads to tree-level 5-point amplitude in eikonal approximation in a generic supertranslated vacuum. The subleading soft graviton theorem follows naturally from the on-shell action when the BMS group is extended to include superrotations. An infinite tower of Goldstone modes is proposed by `generalizing' the Geroch tensor to incorporate a set of divergence-free symmetric traceless tensors on the sphere. This generalization leads to $\text{sub}^{n}$-leading soft insertions in the tree-level $\mathcal{S}$ matrix, thus paving the way to understanding the infinite tower of tree-level symmetries within this framework.