Celestial $Lw_{1+\infty}$ Symmetries and Subleading Phase Space of Null Hypersurfaces

TL;DR

The paper develops a Weyl-covariant framework to study gravity near null hypersurfaces, establishing a dictionary between metric and Newman-Penrose formalisms and mapping the radiative phase space at null infinity to a subleading horizon phase space. It derives a Weyl-covariant recursion for horizon charges, constructs a tower of subleading spin-s charges, and identifies their integrated fluxes as canonical generators of the celestial $Lw_{1+\infty}$ symmetries at the horizon, with a concrete self-dual Kleinian Taub-NUT example. A partially off-shell conformal compactification connects the null-infinity peeling structure to horizon Taylor expansions, allowing the Ashtekar-Streubel symplectic structure to emerge in the self-dual sector at finite distance. The results illuminate how horizon radiation and conserved charges are encoded in a unified radiative-phase-space picture, with potential implications for Carrollian/celestial holography and black hole microstate discussions.

Abstract

Pursuing our analysis of [1], we study the gravitational solution space around a null hypersurface in the bulk of spacetime, such as a black hole or a cosmological horizon. We discuss the corresponding characteristic initial value problem both in the metric and Newman-Penrose formalisms, and establish an explicit dictionary between the two. This allows us to identify Weyl-covariant structures in the solution space, including hierarchies of recursion relations encoding the flux-balance laws. We then establish a correspondence between the gravitational phase space at null infinity and the subleading phase space around the null hypersurface at finite distance. This connection is naturally formulated within the Newman-Penrose formalism by performing a partially off-shell conformal compactification and identifying the analogue of the Ashtekar-Streubel symplectic structure in the radial expansion near the null hypersurface. Using this framework, we identify the celestial $Lw_{1+\infty}$ symmetries in the subleading phase space at finite distance by constructing their canonical generators and imposing self-duality conditions. This allows us to define a notion of covariant radiation, whose absence gives rise to an infinite tower of conserved charges, revealing physical quantities relevant to observers near black hole or cosmological horizons. As a concrete illustration, we consider the case of the self-dual Taub-NUT black hole.