We prove a nonlinear characteristic Cᵏ-gluing theorem for vacuum gravitational fields in Bondi gauge for a class of characteristic hypersurfaces near static vacuum n-dimensional backgrounds, n≥ 3, with any finite k, with cosmological constant Λ ∈ R, near Birmingham-Kottler backgrounds. This generalises the C²-gluing of Aretakis, Czimek and Rodnianski, carried-out near light cones in four-dimensional Minkowski spacetime.
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Chruściel et al. (2024) studied this question.
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