Twistors, charge structure, and BMS symmetries

TL;DR

This paper explores the deep connection between twistors and BMS symmetries in asymptotically-flat spacetimes, formalizing the relationship and providing new insights into the structure of BMS charges using twistorial methods.

Contribution

It establishes an isomorphism between flat spacetime twistors and those on radiation-free sections of null infinity, linking twistorial charges to BMS symmetries and radiative phase space.

Findings

Demonstrates an isomorphism between flat and radiation-free twistor spaces.

Reinterprets Dray-Streubel charge as a gauge-invariant part of Penrose's twistorial charge.

Provides a twistorial framework for analyzing radiative data on null infinity.

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 $\mathscr{I}^+$.