Sub-subleading Soft Graviton Theorem from Asymptotic Einstein's Equations

TL;DR

This paper derives the sub-subleading soft graviton theorem from Einstein's equations by identifying an asymptotic spin-2 charge, revealing a non-local symmetry at null infinity and connecting it to conservation laws and Ward identities.

Contribution

It establishes a direct link between asymptotic Einstein equations and the sub-subleading soft graviton theorem, introducing a new spin-2 charge and its associated non-local symmetry.

Findings

Identification of an asymptotic spin-2 charge in Einstein gravity.

Derivation of the sub-subleading soft theorem from conservation of this charge.

Unified framework for soft theorems as conservation laws of canonical generators.

Abstract

We identify in Einstein gravity an asymptotic spin-$2$ charge aspect whose conservation equation gives rise, after quantization, to the sub-subleading soft theorem. Our treatment reveals that this spin-$2$ charge generates a non-local spacetime symmetry represented at null infinity by pseudo-vector fields. Moreover, we demonstrate that the non-linear nature of Einstein's equations is reflected in the Ward identity through collinear corrections to the sub-subleading soft theorem. Our analysis also provides a unified treatment of the universal soft theorems as conservation equations for the spin-0,-1,-2 canonical generators, while highlighting the important role played by the dual mass.