$w_{1+\infty }$ as the Frame Algebra of Kerr Soft Dressing

Abstract

The Veneziano--Vilkovisky supertranslation is the residual large diffeomorphism relating the canonical Bondi frame to the intrinsic frame of the scattering bodies. We show it leads a tower selected by the exponentiating soft expansion, the object generating the Kerr multipoles at three points. Since \(e^{\eta\omega a\cdot q}\) splits into even and odd parts, the tower alternates parity, and for aligned spin we solve it to all orders in hyperbolic integrals. After a chiral projection its composition law is the classical $w_{1+\infty }$ bracket: the physical content we assign to that algebra.

Comments: 9 pages, 1 figure + Supplemental Material