Twistors, charge structure, and BMS symmetries

Abstract

Corresponding to the Bondi-Metzner-Sachs (BMS) symmetry algebra of asymptotically-flat spacetimes are a set of BMS charges. These are formally constructed via the symplectic formalism of Wald and Zoupas, but the same charge expression may be arrived at by the simpler twistorial procedure of Dray and Streubel. Here, we formalize the connection between twistors and asymptotic symmetries which underlies the Dray-Streubel charge by demonstrating an isomorphism between twistors in flat spacetime and twistors on radiation-free sections of $\mathscr{I}^+$. In the corresponding formalism, the Dray-Streubel charge finds a natural reinterpretation as exactly the part of Penrose's twistorial charge which is invariant with respect to a certain gauge transformation. Furthermore, we argue that the twistorial picture of the radiative phase space, properly formalized, provides a tool alongside the symplectic formalism or shear structure for analyzing radiative data on $\mathscr{I}^+$.