BMS Supertranslations and Not So Soft Gravitons

TL;DR

This paper demonstrates that BMS supertranslations can derive the full tree-level soft graviton theorem without superrotations, linking asymptotic charges to soft theorems in gravity.

Contribution

It shows how BMS supertranslations alone can reproduce the entire tree-level soft graviton theorem, extending the connection between asymptotic symmetries and soft theorems in gravity.

Findings

Soft graviton theorem derived from BMS supertranslation charge

No need for superrotations in deriving the theorem

Method applicable at three orders of the soft expansion

Abstract

In a previous article, we have argued that Low's sub-leading soft photon theorem can be recovered as a Ward identity associated to the same large gauge transformations that control the leading piece of the theorem. The key for that was to link the energy expansion displayed in the soft theorem to a $\frac{1}{r}$ expansion that we can perform in the associated asymptotic charge. We expect this idea to be valid in general, and here we provide compelling evidence for it by showing how the same method works in the case of Einstein-Hilbert gravity. More precisely, we are able to derive the three orders of the tree-level soft graviton theorem simply from the BMS supertranslation charge, known to give rise to the leading soft graviton theorem. In particular, we do not need to invoke superrotations (nor extended superrotations) at any point of the argument.