Quasi-Local Celestial Charges and Multipoles

TL;DR

This paper generalizes quasi-local mass to include higher-spin celestial charges, relating them to multipoles and symmetries in spacetimes, with explicit formulas and flux laws derived from twistor theory.

Contribution

It introduces a geometric framework for celestial symmetries and multipoles using twistor solutions, extending Penrose's mass to higher spins and deriving flux laws.

Findings

Explicit formulas for higher-spin charges on finite surfaces

A phase-space derivation connecting twistor space and spacetime

Relation of celestial symmetries to self-dual gravity integrability

Abstract

We extend Penrose's quasi-local mass definition to include higher-spin charges associated with the celestial $Lw_{1+\infty}$ symmetries and relate them to traditional definitions of multipoles. The resulting formulae provide explicit expressions that can be computed on finite 2-surfaces, given a choice of null hypersurface. They yield a geometric definition of celestial symmetries and multipoles in generic spacetimes in terms of higher-valence solutions to the twistor equations. This, in turn, gives rise to natural flux-balance laws along the null hypersurface. We also present a first-principles phase-space derivation of these charges, starting from a twistor space action for self-dual gravity that can be identified with the standard gravitational asymptotic phase space at null infinity, performing a large gauge transformation analysis and using the Penrose transform to connect with the corresponding spacetime expressions. Finally, we formulate the spacetime analysis in the Plebanski gauge and relate the celestial symmetries to the integrability of self-dual gravity in the case of a self-dual background.