Celestial Lw 1+∞ charges from a twistor action

Abstract

Abstract The celestial Lw 1+∞ symmetries in asymptotically flat spacetimes have a natural geometric interpretation on twistor space in terms of Poisson diffeomorphisms. Using this framework, we provide a first-principle derivation of the canonical generators associated with these symmetries starting from the Poisson BF twistor action for self-dual gravity. We express these charges as surface integrals over the celestial sphere in terms of spacetime data at null infinity. The connection between twistor space and spacetime expressions at I $$ \mathcal{I} $$ is achieved via an integral formula for the asymptotic Bianchi identities due to Bramson and Tod. Finally, we clarify how Lw 1+∞ transformations are symmetries of gravity from a phase space perspective by showing the invariance of the asymptotic Bianchi identities.

Keywords

• Classical Theories of Gravity
• Gauge Symmetry
• Global Symmetries
• Space-Time Symmetries