A twistorial description of BMS symmetries at null infinity

TL;DR

This paper introduces a new twistorial framework for describing BMS symmetries at null infinity, revealing that BMS twistors act as 'square roots' of these symmetries and are characterized by covariant spinor equations.

Contribution

It presents the first twistorial construction of BMS symmetries at null infinity, defining BMS twistors and demonstrating their role as generators of BMS symmetries in asymptotically flat spacetimes.

Findings

BMS twistors form an infinite-dimensional space.

Symmetric tensor products of BMS twistors generate BMS symmetries.

BMS twistor equations are covariant and determined by null infinity's universal structure.

Abstract

We describe a novel twistorial construction of the asymptotic BMS symmetries at null infinity for asymptotically flat spacetimes. We define BMS twistors as spinor solutions to some set of components of the usual spacetime twistor equation restricted to null infinity. The space of BMS twistors is infinite-dimensional. We show that given two BMS twistors their symmetric tensor product can be used to generate (complex) vector fields which are the infinitesimal BMS symmetries of null infinity. In this sense BMS twistors are "square roots" of BMS symmetries. We also show that these BMS twistor equations can be written a pair of covariant spinor-valued equations which are completely determined by the intrinsic universal structure of null infinity.