BMS Supertranslations and Not So Soft Gravitons

TL;DR

The paper argues that BMS supertranslations, analyzed within linearized gravity, suffice to derive the leading, sub-leading, and sub-sub-leading tree-level soft graviton theorems as Ward identities, by matching the energy expansion of soft emissions to the 1/r expansion of asymptotic charges. It constructs the 1/r-expanded charges Q^{(0)}, Q^{(1)}, Q^{(2)} from the linearized solution space with scalar matter, and demonstrates order-by-order how these charges reproduce the corresponding soft factors through Ward identities. The approach avoids invoking superrotations and highlights how boundary data at null infinity govern the universal soft behavior up to sub-sub-leading order, with integration constants hinting at possible loop effects. The work strengthens the view of soft theorems as manifestations of asymptotic symmetries and suggests avenues for extension to non-Abelian theories and holographic perspectives, while clarifying the limitations set by boundary conditions in capturing higher-order soft behavior.

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.