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Celestial Lw1+∞ symmetries and subleading phase space of null hypersurfaces

Romain Ruzziconi1,2,* and Céline Zwikel3,4,5,†

  • *Contact author: romainruzziconi@fas.harvard.edu
  • †Contact author: celine.zwikel@college-de-france.fr
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Phys. Rev. D 113, 044067 – Published 25 February, 2026

DOI: https://doi.org/10.1103/hrbd-cmr7

Abstract

Pursuing our analysis of the companion Letter, [Celestial symmetries of black hole horizons, Phys. Rev. D 113, L041504 (2026).], 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 analog of the Ashtekar-Streubel symplectic structure in the radial expansion near the null hypersurface. Using this framework, we identify the celestial Lw1+∞ 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-Newman-Unti-Tamburino black hole.

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Phys. Rev. D 113, 044067– Published 25 February, 2026
  • Received 12 September 2025
  • Accepted 2 January 2026
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