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

TL;DR

This paper explores the phase space of gravitational solutions near null hypersurfaces, revealing celestial symmetries and conserved charges relevant for horizons, with a detailed analysis using Newman-Penrose formalism and specific black hole examples.

Contribution

It establishes a detailed correspondence between null infinity and finite null hypersurfaces, identifying celestial $Lw_{1+ abla}$ symmetries in the subleading phase space.

Findings

Identification of Weyl-covariant structures and recursion relations

Construction of celestial $Lw_{1+ abla}$ symmetry generators

Infinite tower of conserved charges near horizons

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.