  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.
