Charges for Hypertranslations and Hyperrotations

Abstract

Hypertranslations and hyperrotations are asymptotic symmetries of flat space, on top of the familiar supertranslations and superrotations. They were discovered in arXiv:2205.01422 by working in the Special Double Null (SDN) gauge, where $\mathscr{I}^{+}$ and $\mathscr{I}^{-}$ are approached along $null$ directions. It was observed there that while the hair degrees of freedom associated to these diffeomorphisms show up in the covariant surfaces charges, the diffeomorphisms themselves do not. This made their status intermediate in some ways between global symmetries and trivial gauge transformations, making interpretation ambiguous. In this paper, we revisit the fall-offs considered in arXiv:2205.01422 which were strictly subleading to Minkowski in conventional double null coordinates. We identify a new class of fall-offs where this assumption is relaxed, but whose charges nonetheless remain finite. Remarkably, the leading behavior is still Riemann flat, indicating that these are soft modes. With this more refined definition of asymptotic flatness, we show that leading hypertranslations and leading hyperrotations explicitly show up in the charges. This makes them genuine global symmetries of asymptotically flat Einstein gravity in the SDN gauge. We write down the new algebra of asymptotic Killing vectors that subsumes the BMS algebra.