Superrotations are Linkages

TL;DR

This paper demonstrates that superrotation charges in asymptotic symmetries can be described and regularized using geometric conformal completion and linkage methods, providing a unified approach to their calculation.

Contribution

It introduces a geometric approach to describe superrotation charges and applies a regularization procedure to handle divergences at points.

Findings

Superrotation charges can be described via Penrose's conformal completion.

Linkage methods can be used to calculate superrotation charges.

A regularization procedure makes superrotation charges well-defined at points.

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.