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

TL;DR

Addressing the origin of the sub-subleading soft graviton theorem in four-dimensional asymptotically flat spacetimes, the paper identifies a spin-2 asymptotic charge whose conservation, upon quantization, yields the sub-subleading soft factor. It reveals that the corresponding spin-2 symmetry is non-local at null infinity and realized as a pseudo-vector action, with the dual mass contributing to the structure. The analysis shows that Einstein nonlinearity generates collinear corrections to the S^(2) term and provides a unified view of soft theorems as Ward identities for spin-0, -1, -2 generators within the Weyl-BMS framework. The results suggest deep connections to celestial holography and w_{1+∞} symmetries, while leaving open the interpretation of these symmetries in the bulk.

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.