Superrotations are Linkages

TL;DR

This work shows that superrotations, though singular at the poles, can be incorporated into the asymptotic charge framework by extending the Geroch-Winicour linkage to the Penrose conformal completion. By enforcing the gauge condition $X=0$ and applying the Flanagan-Nichols regularization, the otherwise ill-defined superrotation charges become finite and well-defined, with fluxes analyzable via a Wald-Zoupas-like construction. The authors demonstrate that charges and fluxes for superrotations admit a clean geometric expression on null infinity, linking the Bondi-Sachs and Penrose formalisms and offering a robust route to incorporate these symmetries into the radiative phase space. This provides a principled foundation for understanding memory effects, soft theorems, and the role of conformal symmetries in gravitational radiation within asymptotically flat spacetimes.

Abstract

We show that superrotations can be described using the geometric conformal completion method of Penrose. In particular, superrotation charges can be described and calculated using the linkage method of Geroch and Winicour. Whether superrotation charges are calculated using the coordinate based Bondi formalism or the geometric Penrose formalism, the fact that the superrotation blows up at a point makes the superrotation charge formally ill defined. Nonetheless, we show that it can be made well defined through a regularization procedure devised by Flanagan and Nichols.